Instigator / Pro
4
1702
rating
574
debates
67.86%
won
Topic
#157
1/3 is not actually 0.3r and also 1 doesn't equal 0.9r, the reason the misconception of 1/3=0.3r is accepted by mainstream math is due to a flaw in the decimal number system.
Status
Finished
The debate is finished. The distribution of the voting points and the winner are presented below.
Winner & statistics
After 1 vote and with 3 points ahead, the winner is...
Death23
Parameters
- Publication date
- Last updated date
- Type
- Standard
- Number of rounds
- 5
- Time for argument
- Three days
- Max argument characters
- 30,000
- Voting period
- One month
- Point system
- Multiple criterions
- Voting system
- Open
Contender / Con
7
1553
rating
24
debates
56.25%
won
Description
No information
Round 1
r=recurring
1/3 is actually unanswerable. If you really are going to be honest about mathematics, you need to admit there are limitations to it. It is literally 100% identical in the impossibility to answer as getting the even-numbered-root of any negative value. What's the square-root or power-of-four-root of a negative number? Exactly.
There are things in math that result in no answer at all. The reason is that if we were to use binary numbers we'd clearer see how '1' can never ever be broken into 3 parts. '101' would repeat infinitely, yes it's the same thing but what happens is the following:
(1/3)*y SHOULD EQUAL y*1/3
So multiply 0.3r by 30 (not 3, 30). Now multiply 1 by 30 and divide it by 3.
When we make the first number a whole number it becomes quite blatant that 9.Something (in this case 9r) is not equal to 10.Something (in this case 0)
The argument that if you have an infinite series of decimal places that happen to be the same number again and again that it's in any way more real or actualised as a number than a series that alters itself after an infinite number of digits is infantile to say the least and here is why:
If you were a child or someone generally immature when it comes to wisdom and logic, you would maybe thing 'ah so because the final number of .3r is the same as the rest it's somehow not equally impossible to ever get as the last number of pi or the last '1' in the answer to 1-0.9r (it is 0.0r1, the 1 being after a series of infinite 0's).
All irrational numbers (that's what 1/3 is) are actually placeholders for a value that never ever could be real. It doesn't matter how many threes you had, it never ever would be a third of 1, it would ALWAYS be less.
In this round I will argue only
my case. I will not argue against Pro's case. I will argue against Pro's case
in round 2.
The resolution is as follows:
1/3 is not actually 0.3r and also
1 doesn't equal 0.9r, the reason the misconception of 1/3=0.3r is accepted by
mainstream math is due to a flaw in the decimal number system.
Little "r" simply means
repeating. For example, 0.99999 repeating could be expressed as 0.9r. The
resolution contains three separate claims:
A) 1/3 does not equal 0.3r
B) 1 does not equal 0.9r
C) The reason that mainstream
mathematicians accept that 0.3r = 1 is due to a flaw in the decimal number
system.
The resolution claims A, B and
C. In order for me to show that the resolution is false, it isn't necessary for
me to show that A, B and C are all false. Rather, showing that just one of
those claims - A, B or C - is false is sufficient to disprove the resolution.
My argument is as follows: The
resolution is false because claim B is false. (Claim B is that 1 does not equal
0.9r)
Claim B is false because 1, in
fact, does equal 0.9r. I offer the following arguments in support of this
assertion:
1. An algebraic argument -
x = 0.9r
10x = 9.9r mutiplying both sides by 10
10x = 9 + 0.9r separating 0.9r and 9
10x = 9 + x substituting 0.9r with x
9x = 9 by subtracting x from both sides
x = 1 by dividing both sides by 9
2. Another algebraic argument -
1 - 0.9r = 0.0r = 0 ergo 1 = 0.9r
3. An intuitive argument -
There's no value so close to 1
such that you can't fit another value half way between it and 1. For example,
suppose we thought 0.999 was the closest number to 1. We would have thought
wrong as 0.9995 is halfway between 0.999 and 1.
If 0.9r were less than 1 then you
could fit another value halfway in between 0.9r and 1. For example, 0.9r5. But
this can't be done because the 9's go on infinitely. You would have to get past
the 9's to fit the 5. You can't get past the 9's.
Round 2
Pro is copying himself so I will do it to myself too. Credit to myself in this debate: https://www.debateart.com/debates/146
I notice that Pro forgot to define 'equals' so I will provide that definition by making a hybrid definition based on 2 links.
Being identical with what is about to be or has just been mentioned in quantity, size, degree, or value.
Let's debunk Pro's case now.
x = 0.9r10x = 9.9r mutiplying both sides by 1010x = 9 + 0.9r separating 0.9r and 910x = 9 + x substituting 0.9r with x9x = 9 by subtracting x from both sidesx = 1 by dividing both sides by 9
Alright, so here is where we will turn Pro's disproof of me against Pro himself/herself.
Pro is denying that the difference between 1 and 0.9r is existent at all. The difference is 0.0r1 (the 1 is going to happen after an infinite number of 0's).
This value: 0.0r1 is argued by people on the side of Pro as being too irrational or far from real consideration because the 1 follows a series of infinite 0's which thus are never going to actually become the 1.
So when Pro multiplies 0.9r by 10 in order to ascertain what 10x (x=0.9r) is, Pro defeats their aforementioned attack on Con and here is why:
To multiply by 10, there must be a 0 placeholding the final number of the number being multiplied by that 10. In this case, that final number is 9. In reality 0.9r is actually able to be written as 0.9r9 because it is a series of infinite 9's with a number 9 at the end just the same in significance as the 1 at the end of 0.0r1 which is the difference between 0.9r and 1 and which Pro is denying is to be considered existent at all. Thus, if we are to multiply 0.9r by 10 either we can't do that since it will actually be 9.9r0 and the 0 will never ever come to be just as the 1 would never come to be in 0.0r1 or we admit that 0.0r1 matters as an actual value and then we concede that the resolution is false.
1 - 0.9r = 0.0r = 0 ergo 1 = 0.9r
This is a lie.
1 - 0.9r = 0.0r1 =/= 0.0r
(=/= means 'is not equal to' and/or 'doesn't equal')
There's no value so close to 1 such that you can't fit another value half way between it and 1. For example, suppose we thought 0.999 was the closest number to 1. We would have thought wrong as 0.9995 is halfway between 0.999 and 1.If 0.9r were less than 1 then you could fit another value halfway in between 0.9r and 1. For example, 0.9r5. But this can't be done because the 9's go on infinitely. You would have to get past the 9's to fit the 5. You can't get past the 9's.
0.9r05 (not 0.9r5) is the actual midpoint between 0.9r and 1 (I said this in comments section long before Pro posted their Round, check timestamps, this was a blitz-debate where Pro replied in only 2 hours so I replied as quick as I could in the comments about the clarification?). This changes NOTHING about the point I was making but it's wrong to call 0.9r5 the midpoint, I admit that.
0.9r9 is as irrational a number as 0.0r1. Just because the string of infinite 9s ends in a 9 doesn't at all make it less irrational. The number being the same as those preceding it doesn't make it any less attainable, this is an illusion... A Parlour/Parlor Trick if you will.
Either Pro admits 0.9r(ending in a 9) is impossible to be a number and therefore can't equal 1 or Pro concedes that the 0.0r(ending in a 1) is an actual number and therefore the difference between 0,9r and 1 is real.
In this round I will argue only against Pro's round 1
arguments.
In general, Pro argues that the resolution is true because it's paradoxical for the sum of an infinite series number to result in a finite number. Pro supports this argument with the fact that it's not possible to get to infinity and contrasts this with the finite nature of natural numbers.
The paradox presented by Pro is resolvable. It isn't necessary for an infinite series to "get to infinity"; The challenge isn't to "get to infinity" but merely to answer this question - "What would the value of an infinite series be supposing it somehow got to infinity?" The answer to that is calculable in many cases as I have shown in my round 1 arguments. The sum of an infinite series may result in a finite value. This may happen when, for example, the number keeps getting larger but each time it gets larger the additional value is reduced (e.g. 0.9 + 0.09 + 0.009...). In a sense, there is the infinitely getting bigger component but there is also the infinitely getting smaller part. The two infinities work against one another, somewhat canceling each other out and the result is a finite convergence.
Aside from the general argument, Pro makes many baseless claims in his round 1 argument which should be rejected, e.g. -
A) The value of 0.3r is "100% identical in the impossibility to answer as getting the even-numbered-root of any negative value."
B) 1 can never ever be broken into 3 parts
C) it is "quite blatant that [9.9r] ... is not equal to [10.0r]"
D) the contention that there's a true sum for an infinite series of decimals is infantile
E) Straw man argument. "you would maybe thing 'ah so because the final number of .3r is the same as the rest it's somehow not equally impossible to ever get as the last number of pi or the last '1' in the answer to 1-0.9r (it is 0.0r1, the 1 being after a series of infinite 0's)."
I challenge all of these claims and other similar round 1 claims as unsubstantiated.
In general, Pro argues that the resolution is true because it's paradoxical for the sum of an infinite series number to result in a finite number. Pro supports this argument with the fact that it's not possible to get to infinity and contrasts this with the finite nature of natural numbers.
The paradox presented by Pro is resolvable. It isn't necessary for an infinite series to "get to infinity"; The challenge isn't to "get to infinity" but merely to answer this question - "What would the value of an infinite series be supposing it somehow got to infinity?" The answer to that is calculable in many cases as I have shown in my round 1 arguments. The sum of an infinite series may result in a finite value. This may happen when, for example, the number keeps getting larger but each time it gets larger the additional value is reduced (e.g. 0.9 + 0.09 + 0.009...). In a sense, there is the infinitely getting bigger component but there is also the infinitely getting smaller part. The two infinities work against one another, somewhat canceling each other out and the result is a finite convergence.
Aside from the general argument, Pro makes many baseless claims in his round 1 argument which should be rejected, e.g. -
A) The value of 0.3r is "100% identical in the impossibility to answer as getting the even-numbered-root of any negative value."
B) 1 can never ever be broken into 3 parts
C) it is "quite blatant that [9.9r] ... is not equal to [10.0r]"
D) the contention that there's a true sum for an infinite series of decimals is infantile
E) Straw man argument. "you would maybe thing 'ah so because the final number of .3r is the same as the rest it's somehow not equally impossible to ever get as the last number of pi or the last '1' in the answer to 1-0.9r (it is 0.0r1, the 1 being after a series of infinite 0's)."
I challenge all of these claims and other similar round 1 claims as unsubstantiated.
Round 3
Con states the following:
It isn't necessary for an infinite series to "get to infinity"; The challenge isn't to "get to infinity" but merely to answer this question - "What would the value of an infinite series be supposing it somehow got to infinity?"
This concedes that the 0.0r1 difference between 0.9r and 1 is a valid value. It also then proves that since 0.3r multiplied by 3 is not 3/3 but rather (2.9r7)/3, that it cannot possibly be a third of 1.0r
In this round I will respond only to Pro's round 2 arguments. In the prior debate, Pro was Con. In the quoted text below, Pro/Con references may be switched, but I have made my responses here consistent with Pro/Con in this debate.
I notice that Pro forgot to define 'equals' so I will provide that definition by making a hybrid definition based on 2 links.Being identical with what is about to be or has just been mentioned in quantity, size, degree, or value.
I
agree with Pro's purported definition of "equals" with the reservation
that as applied here the appropriate reference would be to quantity or
value.
Let's debunk Pro's case now.x = 0.9r10x = 9.9r mutiplying both sides by 1010x = 9 + 0.9r separating 0.9r and 910x = 9 + x substituting 0.9r with x9x = 9 by subtracting x from both sidesx = 1 by dividing both sides by 9Alright, so here is where we will turn Pro's disproof of me against Pro himself/herself.Pro is denying that the difference between 1 and 0.9r is existent at all. The difference is 0.0r1 (the 1 is going to happen after an infinite number of 0's).This value: 0.0r1 is argued by people on the side of Pro as being too irrational or far from real consideration because the 1 follows a series of infinite 0's which thus are never going to actually become the 1.So when Pro multiplies 0.9r by 10 in order to ascertain what 10x (x=0.9r) is, Pro defeats their aforementioned attack on Con and here is why:To multiply by 10, there must be a 0 placeholding the final number of the number being multiplied by that 10. In this case, that final number is 9. In reality 0.9r is actually able to be written as 0.9r9 because it is a series of infinite 9's with a number 9 at the end just the same in significance as the 1 at the end of 0.0r1 which is the difference between 0.9r and 1 and which Pro is denying is to be considered existent at all. Thus, if we are to multiply 0.9r by 10 either we can't do that since it will actually be 9.9r0 and the 0 will never ever come to be just as the 1 would never come to be in 0.0r1 or we admit that 0.0r1 matters as an actual value and then we concede that the resolution is false.
Pro's alleged
debunking may be soundly rejected as it's not consistent with the idea
of infinity. Infinity isn't a number. It's an idea and by its definition
it has no end - And consequently no "after". For that reason, Pro's
arguments are fatally flawed.
With
the first algebraic argument Pro claims that multiplying 0.9r by 10
results in 9.9r0 rather than 9.9r and that the algebraic reasoning is
flawed as a result. ("there must be a 0 placeholding the final number")
This is incorrect as it's logically inconsistent with the idea of infinity. By definition, infinity has no end and consequently there is no "after" with something infinite. There
is no 0 after 9.9r because there is no "after" in the case of an
infinitely long sequence. There is no "final number". Infinity goes on
forever. The hypothetical placeholder 0 supposed by Pro can't and doesn't happen as it's a logical impossibility.
1 - 0.9r = 0.0r = 0 ergo 1 = 0.9rThis is a lie.1 - 0.9r = 0.0r1 =/= 0.0r(=/= means 'is not equal to' and/or 'doesn't equal')
Pro's
claim that I lied is baseless. Deception isn't evident here. In fact,
there is evidence that I actually do believe what I'm saying. I'll show
you - Consider the comments I made in debate 130 - https://www.debateart.com/debates/130 - Those comments predate this debate and indicate a belief that I
personally agree with this resolution and specifically my second
algebraic argument. In those comments I stated that "1 - 0.999(r) =
0.000(r) = 0 ergo 1 = 0.999(r)". I had no reason to lie there and
there's no indication that I've changed my mind in the interim.
Pro's argument here is that 0.9r = 0.0r1. This is not true. This is incorrect as it's logically inconsistent with the idea of infinity. By definition, infinity has no end and consequently there is no "after" with something infinite. There
is no 1 after 0.0r because there is no "after" in the case of an
infinitely long sequence. There is no "final number". Infinity goes on
forever. The hypothetical 1 occurring after 0.0r supposed by Pro can't and doesn't happen as it's a logical impossibility.
There's no value so close to 1 such that you can't fit another value half way between it and 1. For example, suppose we thought 0.999 was the closest number to 1. We would have thought wrong as 0.9995 is halfway between 0.999 and 1.If 0.9r were less than 1 then you could fit another value halfway in between 0.9r and 1. For example, 0.9r5. But this can't be done because the 9's go on infinitely. You would have to get past the 9's to fit the 5. You can't get past the 9's.0.9r5 actually is half way between 0.9r9 and 1. You are forgetting that the 9 at the end of the series is just as impossible to reach as the 5 at the end of those 9's. Either you are denying 0.9r9 ever reaches the last 9 and thus are claiming it doesn't exist and thus can't be equal to 1 which does exist as a number or you admit that 0.9r5 is indeed what you just said we would have thought.
Pro's
response to my intuitive argument similarly fails. Pro claims that
"0.9r5 actually is half way between [0.9r] and 1." This number supposed
by Pro - 0.9r5 - is a logical impossibility and can't exist. 0.9r5
requires there to be an "after" with an infinitely long sequence of 9's.
There is no after with infinity. Pro's claim of equivalence between my
arguments and his (e.g. "the 9 at the end of the series is just as
impossible to reach as the 5") are false. I never claimed to reach the 9
at the end of the series. There is no end to the series. The end of Pro's final argument is a lengthy false dilemma. This form of argument
is known to be fallacious. https://en.wikipedia.org/wiki/False_dilemma
Round 4
In this debate I never ever said that 0.9r5 was the midpoint, fail copy pasting. I correct myself before Con pasted the 'error' because I knew he'd paste it.
0.9r05 is the midpoint as the (05) becomes the '10' to then be the '1' in 0.0r1 which is the difference between 0.9r and 1.0r
Anyway, let's stick to the topic.
The classic argument people make that seems irrefutable isn't the 10x one that Con did but rather the trickier illusion of:
1.3 = 0.3r (which mainstream math, especially that taught at a high-school level considers to be correct)
Based on this lie, it then says that since 0,3r*3 = 0.9r and 1/3*3 = 3/3 that there's a connection to be drawn to make 0.9r = 1.
THIS IS A LIE!!!!!!!
Not the connection, no. I will show the lie:
1/3 is an impossible value. This is something we have to ACCEPT. 1/3 does not exist beyond an idea or symbol we could invent for it like we did for pi. The actual number can never ever be written in full because you'll never get past the 3's to read the 'third of 1' to add onto them.
1 doesn't split into 3 parts because 10 doesn't and to make the '1' you need a split. This is why you can find the midpoint between 0,9r and 1 since 05*2 = 10 to become the 1 difference to turn it into 1 but why you can never ever make a third of one be an actual number. Yes, even a calculator will give you 0.3r as the answer because a calculator is PROGRAMMED BY the people who have this delusion and rely on long-division as their way of approaching a division sum when in fact the way to 'divide' is simply to ask 'is there a number that multiplied by the divisor (in this case 3) gets us to the result of '1'?' THE ANSWER IS NO!!!!!!
1/3 doesn't exist in the real-value number system and Con has refused to address this despite explicitly promising to in an earlier Round.
Con says the following:
It isn't necessary for an infinite series to "get to infinity"; The challenge isn't to "get to infinity" but merely to answer this question - "What would the value of an infinite series be supposing it somehow got to infinity?"
But then Con concedes the following:
This concedes that the 0.0r1 difference between 0.9r and 1 is a valid value. It also then proves that since 0.3r multiplied by 3 is not 3/3 but rather (2.9r7)/3, that it cannot possibly be a third of 1.0r
Because of the following:
The argument that if you have an infinite series of decimal places that happen to be the same number again and again that it's in any way more real or actualised as a number than a series that alters itself after an infinite number of digits is infantile to say the least and here is why:If you were a child or someone generally immature when it comes to wisdom and logic, you would maybe thing 'ah so because the final number of .3r is the same as the rest it's somehow not equally impossible to ever get as the last number of pi or the last '1' in the answer to 1-0.9r (it is 0.0r1, the 1 being after a series of infinite 0's).All irrational numbers (that's what 1/3 is) are actually placeholders for a value that never ever could be real. It doesn't matter how many threes you had, it never ever would be a third of 1, it would ALWAYS be less.
In this debate I never ever said that 0.9r5 was the midpoint, fail copy pasting. I correct myself before Con pasted the 'error' because I knew he'd paste it.0.9r05 is the midpoint as the (05) becomes the '10' to then be the '1' in 0.0r1 which is the difference between 0.9r and 1.0rAnyway, let's stick to the topic.The classic argument people make that seems irrefutable isn't the 10x one that Con did but rather the trickier illusion of:[1/3] = 0.3r (which mainstream math, especially that taught at a high-school level considers to be correct)Based on this lie, it then says that since 0,3r*3 = 0.9r and 1/3*3 = 3/3 that there's a connection to be drawn to make 0.9r = 1.THIS IS A LIE!!!!!!!Not the connection, no. I will show the lie:1/3 is an impossible value. This is something we have to ACCEPT. 1/3 does not exist beyond an idea or symbol we could invent for it like we did for pi. The actual number can never ever be written in full because you'll never get past the 3's to read the 'third of 1' to add onto them.1 doesn't split into 3 parts because 10 doesn't and to make the '1' you need a split. This is why you can find the midpoint between 0,9r and 1 since 05*2 = 10 to become the 1 difference to turn it into 1 but why you can never ever make a third of one be an actual number. Yes, even a calculator will give you 0.3r as the answer because a calculator is PROGRAMMED BY the people who have this delusion and rely on long-division as their way of approaching a division sum when in fact the way to 'divide' is simply to ask 'is there a number that multiplied by the divisor (in this case 3) gets us to the result of '1'?' THE ANSWER IS NO!!!!!!1/3 doesn't exist in the real-value number system and Con has refused to address this despite explicitly promising to in an earlier Round.
Pro is overly emphasizing the importance of 1/3. My case against the resolution has nothing to do with 1/3 and everything to do with 1 = 0.9r. Even if I drop the argument, it doesn't matter. What ultimately matters is that Pro must prove the entirety of the resolution to be true in order to win, not just the 1/3 issue.
Nonetheless, I will address these points. Pro would have us believe that 1/3 is an impossible value, but it isn't. 1/3 can be written in full, easily if you use a different base number system. First, writing 1/3 as 1/3 is writing it in full. Second, supposing you had a base 3 number system (i.e. count like 0 1 2 10 11 12 20 21 22 100...) then you could write 1/3 as 0.1. Alternatively, you could use a base 9 number system (i.e. count like 012345678-10), then 1/3 could be written as 0.3.
Con says the following:It isn't necessary for an infinite series to "get to infinity"; The challenge isn't to "get to infinity" but merely to answer this question - "What would the value of an infinite series be supposing it somehow got to infinity?"
But then Con concedes the following:This concedes that the 0.0r1 difference between 0.9r and 1 is a valid value. It also then proves that since 0.3r multiplied by 3 is not 3/3 but rather (2.9r7)/3, that it cannot possibly be a third of 1.0r
Pro states that there was a concession. There wasn't, and no argument was dropped. In round 3, I stated specifically that "In this round I will respond only to Pro's round 2 arguments."
Because of the following:The argument that if you have an infinite series of decimal places that happen to be the same number again and again that it's in any way more real or actualised as a number than a series that alters itself after an infinite number of digits is infantile to say the least and here is why:If you were a child or someone generally immature when it comes to wisdom and logic, you would maybe thing 'ah so because the final number of .3r is the same as the rest it's somehow not equally impossible to ever get as the last number of pi or the last '1' in the answer to 1-0.9r (it is 0.0r1, the 1 being after a series of infinite 0's).All irrational numbers (that's what 1/3 is) are actually placeholders for a value that never ever could be real. It doesn't matter how many threes you had, it never ever would be a third of 1, it would ALWAYS be less.
This is largely a straw man argument, and 1/3 is not an irrational number. 1/3 is a rational number - a real number. The mathematical definition of a rational number is "any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q." Real numbers are the numbers that can represent distance on a number line. Irrational numbers are all the real numbers which are not rational numbers (e.g. pi). https://en.wikipedia.org/wiki/Rational_number
Round 5
I said all that had to be said
Pro has dropped the arguments.
==================================================================
>Reported vote: SupaDudz // Moderator action: Removed<
3 points to Con (arguments). Reasons for voting decision: I was very close to voting PRO throughout the debate, but RM decides to concede the rebuttals in Round 5 with a stupid saying. Darn... I vote CON because PRO concedes all r5 and Deaths rebuttals
[*Reason for removal*] The voter needs to explain which rebuttal that Pro conceded was sufficient to win Con the debate. It is not enough to say *that* Pro conceded Con’s R4. This would be analogous to giving argument points to one side because the other side forfeited one round out of five and the entire RFD being "forfeit."
==================================================================
Not at all, I made a flawless one.
I read what you wrote, it’s not that I don’t understand, but that I understood and found that your opponent did much better. His explanation of infinite series was good.
Perhaps next time you should make a better argument.
Why did he? Did you even read what I wrote?
That was a typo on my part- I meant con explained it very well.
You have no idea what you are doing or how to think
You spend the whole last sentence complimenting me and vote con thank you very little
You didnt. And it was clear from your opponents argument that this was just a typo on his part.
When the fuck did I say 0.9r = 0.0r1
Just stop this low Iq voter cult. Pass a quiz to vote please.
*******************************************************************
>Reported Vote: Ramshutu // Mod action: Not Removed
>Points Awarded: 3 points to Con for arguments
>Reason for Decision: The whole debate from both pro and con break down into a discussion about infinite number series. Con makes a series of arguments about infinite number series, and argues what they actually mean, the best summary from his arguments was.
“Pro's argument here is that 0.9r = 0.0r1. This is not true. This is incorrect as it's logically inconsistent with the idea of infinity. By definition, infinity has no end and consequently there is no "after" with something infinite. There is no 1 after 0.0r because there is no "after" in the case of an infinitely long sequence. There is no "final number". Infinity goes on forever. The hypothetical 1 occurring after 0.0r supposed by Pro can't and doesn't happen as it's a logical impossibility.”
This on its own, wins the debate for con on arguments. This convincingly shows both the reason why pros arguments around number series is wrong, and demonstrates why (despite it being non intuitive), 0.9r = 1.
Pros entire argument effectively relates to variations on a theme to there being a number between 0.9r and 1, which requires them to hold different values: con shows this to be false with his explanation of infinite’s and number sequence. Pro doesn’t provide any convincing rebuttal of this silver bullet argument. Both pros mathematical and “intuitive” arguments were very, very well explained.
>Reason for Mod Action: The debate clearly surveys the main arguments and weighs them to reach a sufficient verdict.
************************************************************************
I'll try to read it to see if i understand. Numbers just scare me so i didn't read it knowing i'd probably not understand anything if it has to do with math... logic is a different issue so let me see.
This is actually pure logic debate (in both of our eyes the other is absolutely wrong) and not a knowledge-heavy one at all.
I'm not qualified to vote for this debate... but interesting topic.
yes tyvm
I'll be working on it this weekend.
you as well (read previous comment)
You are tagged as I believe this debate will both interest you and because you are a good voter (or maybe only 1 of these 2). Please read and keep an open mind and note: ROUND 5 WAS NOT ME CONCEDING, it was because I genuinely had nothing left to say (Con was repreating themselves in R4 and I have already rebuked it all).
You are wrong.
First example number: 0.0r1 - A logically impossible number as it supposes a point beyond infinity.
Second example number: 0r1 - A logically possible number as it doesn't suppose a point beyond infinity. The "1" here is where infinity begins, not beyond a supposed end.
So we agree that endless digits behind a number is just as illogical as endless digits before a number?
Infinite - There is no number so close to infinity such that you can't multiply it by 2 and have a new number larger still. Therefore, there is no closest number to infinity. Is that not what an infinite number supposedly is? Or rather, is that not what 0.9r is? A number infinitely close to 1 but not at 1? Such a number isn't logically possible because it's existence isn't consistent with the foregoing reasoning excluding such a number's existence.
Re: Infinitesimals - There is no number so close to 0 such that you can't divide it by 2 and have a new number smaller still. Therefore, there is no closest number to 0. Is that not what an infinitesimal supposedly is? Or rather, is that not what 0.0r1 supposedly is? A number infinitely close to 0 but not at 0? Such a number isn't logically possible because it's existence isn't consistent with the foregoing reasoning excluding such a number's existence.
Re: "The question" - This is a loaded question. The question contains the assumption that "one direction [... is] more logical than the other". That assumption is false.
"...the possibility of such a remainder is eliminated by the logical impossibility of infitesimals."
and
The question of how is one direction (of endless digits) more logical than the other?
Which position are you referring to?
Ok, I gathered as much from your previous comments.
Can you present any logical reasoning in support of your position?
I don't think that.
Why would you think it might be more logical for the zeroes to extend endlessly in one direction, but not in the other direction?
How is one direction more logical than the other?
It's not. Why does that matter?
How is it "more impossible" for "infinity" to be before a number instead of after a number?
When you write a 1, isn't it implied that there is an infinite number of zeroes both before and after the 1?
r0000000000000000001.00000000000000r ?
then .3r is impossible and so is 0.9r
There's no remainder. It converges at infinity. Any theoretical remainder would have to be infinitesimal, but the possibility of such a remainder is eliminated by the logical impossibility of infitesimals.
Certainly 0.9r ROUNDS to 1. However, in the "real world" you have to add something to 0.9r in order for it to actually cross the line between 0.9r and 1.
The smaller the increment, the more accurate your result will be, but there is a very real practical limit to how small of an increment can be realistically added.
And so, we end up with a precision problem. Certainly there may be some theoretical "remainder", but if that remainder is beyond our scope of measure, it is de-facto meaningless.
They get infinitesmally large. ;)
Those aren't infinitesimals.
then 1/3 can't exist. Same with 0,9r
Infinitesimals can't exist. You're familiar enough with the arguments to know that.
1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009999999r
=/=
0.9r which makes this a precision problem. The difference between 0.9r and 1 is not zero.
0.9r + 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 = 1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009999999r = 1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
And then if that's true, 0.9r never reaches the last 9 to ever equal 1.
You seem to have failed to properly address Death23's proposed definition of "infinity".
There are recognized situations where "infinity" is treated as a set and you can have two or more "infinities", or even "infinity" + 1.
As a practical matter, anyone could add a... 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 to anyone else's 0.9r and your point of precision would most likely be beyond anyone's practical ability to measure.
For example if I added 0.9r and the very very real number... 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 together, what would the result be?
It would seem to be "1". Therefore the difference between 0.9r and 1.0 is not zero.
Yeah, right.
Everything you brought up was already disproven by my previous rounds beyond any dispute as it's irrefutable fact.
When you fail to respond to an argument, you drop the argument. You failed to respond to my round 4 arguments. Ergo, you dropped those arguments.
I dropped nothing you liar.
Yeah I caught that. It took me a minute or so to figure it out though.
1/3 not 1.3 for that sum at the start of my R4
No: 4.9999r rounds.
5 rounds?