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@zedvictor4
I forgot to add you as a mention in the above post, but it was directed at you.
Math controversy should not exist
Posts
Total:
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@Math_Enthusiast
*If you aren't sure why this implies that infinitesimals can't exist, if a positive infinitesimal is defined as a number greater than zero but less than 1/n for every natural number n, (which 1 - 0.99999... would be if it were positive) than if x is a positive infinitesimal, x < 1/n for every natural number n, and so 1/x > n for every natural number n, a violation of the Archimedean property.
Archimedean Property does not consider laws of thermodynamics. Archimedean property applies a rule of scale and proportion which is not by fact accurate by laws of thermodynamics or in line with human margins of error. 0.9 is proportional to 0.999999 they are equal though are not secureas equal by precise measurements and are subject to change, such low values are demonstrated to change by the choice of letters assigned in Calculus near theend of the English Alphabet.
Lemma The set N of positive integers N = {0, 1, 2, . . .} is not bounded from above.Proof Reasoning by contradiction, assume N is bounded from above. Since N ⊂ R and Rhas the least upper bound property, then N has a least upper bound α ∈ R. Thus n ≤ αfor all n ∈ N and is the smallest such real number.Consequently α − 1 is not an upper bound for N (if it were, since α − 1 < α, then α wouldnot be the least upper bound). Therefore there is some integer k with α − 1 < k. But thenα < k + 1. This contradicts that α is an upper bound for N
Not everyone has or can work an Electron Microscope to establish that there is no natural value of 0.999999 and those values created by computers and calculators are fabricated and not calculated by poor practice in calculation. There are several examples of this throughout the history of mathematics as science has evolved over the years. The formula to write 0.9999 is more complex thus taking more work than that what is for most people is not needed to do to acquire the sum which will suit a given purpose during normal math routines...
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@zedvictor4
It is a concern of both digital money and A.I. As you may be tip toeing around the topic, yes, this math has been a loop hole for many computer programs and even has a name as it can take place as simple data seepage in most programming.
And joke or not. .....It's actually a reasonable consideration, relative to reductionism.
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@John_C_87
Archimedean Property does not consider laws of thermodynamics. Archimedean property applies a rule of scale and proportion which is not by fact accurate by laws of thermodynamics or in line with human margins of error. 0.9 is proportional to 0.999999 they are equal though are not secureas equal by precise measurements and are subject to change, such low values are demonstrated to change by the choice of letters assigned in Calculus near theend of the English Alphabet.
I'm not sure what the sure what any of this has to do with the Archimedean Property. The proof of the Archimedean property is purely done in the abstract mathematical setting with no relation to thermodynamics or physics more generally. For that matter, nothing you present here addresses the proof of the Archimedean property. Also, no, numerical constants don't change. You seem to be referring to measurement error in computers, which is not relevant in the context of pure mathematics, where everything is done rigorously and precisely.
Not everyone has or can work an Electron Microscope to establish that there is no natural value of 0.999999 and those values created by computers and calculators are fabricated and not calculated by poor practice in calculation. There are several examples of this throughout the history of mathematics as science has evolved over the years. The formula to write 0.9999 is more complex thus taking more work than that what is for most people is not needed to do to acquire the sum which will suit a given purpose during normal math routines...
Not only does not everyone have an electron microscope, no one needs one to verify that the proof that you quoted (which is the standard proof of the Archimedean property) is valid. Also, errors in computers and calculators are irrelevant. No computer or calculator is required in this proof.
You have not disproved the Archimedean property. You have mostly just talked about errors in computers, which is irrelevant to this discussion. If you are confident that the Archimedean property is wrong, provide a counterexample:
The Archimedean property states that if x is a real number then n > x for some natural number n. If this is false you should be able to provide a real number x for which I cannot provide a natural number n that is greater than your x.
All you need to respond with is one number. It just takes one number to prove me wrong. Given how well-substantiated this simple mathematical fact is, I am highly doubtful that you will be able to provide such a number.
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@Math_Enthusiast
Not only does not everyone have an electron microscope, no one needs one to verify that the proof that you quoted (which is the standard proof of the Archimedean property) is valid. Also, errors in computers and calculators are irrelevant. No computer or calculator is required in this proof.
"Everyone needs to have an Electron Microscope to observe as a witness the error as it is made in mathematics and how it occurs ,or it is otherwise seen as human failure only."
The idea is not to disprove Archimedean Property, the objectis to establish it is not mathematically relevant. Archimedean Property are classifications of subsets and mathematic elements. The Archimedean Property describes that ( 9.0 ≠ 10 ) as ( 0.9 ≠ 1.0) stating that as fact9.0 and 0.9 are normal subgroup( ⪧) the idea is not to disprove Archimedean Property the object is to establish it is not mathematically used relevant. Archimedean Property are clasifications of subsets and mathematic elements. The Archimedean Property describes that 9 is boundary.
In abstract algebra, a normal subgroup (also known as a invaariant suibgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation by members of the group of which it is a part. In other words,a subgroup N of the group G is normal in Gif and only if gng ^ -1 element (∈) N for all g element (∈ )G and n element ( ∈ )theusual notation for this relation is N normal subgroup (⪦ )G
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@Math_Enthusiast
And I easily demonstrated that 0.9... will always fall .1 or .01 etcetera, short of 1.
No rigour required.
And FLRW and myself understand each other well enough.
I would suggest that their remark was actually aimed at the futility of the ongoing 0.9... issue, and those who like to make it an issue.
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@zedvictor4
And I easily demonstrated that 0.9... will always fall .1 or .01 etcetera, short of 1.
What Archimedean Property displays is that the law of motion applies to numbers by mathematic and mathematic equations. Whereas,( 0.99999) is a subgroup of (9.0), (0.969696) is a normal subgroup of (96.0), (9.0) is not a normal subgroup of (96.0), the four subgroups may be part of a other form of subgroup outside the normal, stating motion. As far as Ebuc what it proves about time is that (0.0166666) is not part of a normal subgroup in mathematics when written as (.0166.99) or( 12: 00: 00: 1.99 what we know about time is that there is no zero in a compass which reads a curved line in relationship to a tangent. This means the calculus is and was always missing key Identificatioin in formal equations. Did not mean to leave you out of the debate Ebuc, always a pleasure.
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@Math_Enthusiast
The fact that the set of all integers contains more terms than the set of all even or odd integers renders the word more (or greater than) meaningless.
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@John_C_87
"Everyone needs to have an Electron Microscope to observe as a witness the error as it is made in mathematics and how it occurs ,or it is otherwise seen as human failure only."
There is no error involved, so I don't see this as relevant. You may claim that 0.99999.. = 1 is dependent on error, but that is simply false. I demonstrated in post #14 that this follows from the definition of an infinite decimal.
The idea is not to disprove Archimedean Property, the objectis to establish it is not mathematically relevant. Archimedean Property are classifications of subsets and mathematic elements. The Archimedean Property describes that ( 9.0 ≠ 10 ) as ( 0.9 ≠ 1.0) stating that as fact9.0 and 0.9 are normal subgroup( ⪧) the idea is not to disprove Archimedean Property the object is to establish it is not mathematically used relevant. Archimedean Property are clasifications of subsets and mathematic elements. The Archimedean Property describes that 9 is boundary.
The Archimedean property states that if x is a real number there exists some natural number n such that n > x, so the Archimedean property has nothing to do with subsets or normal subgroups, nor does it "describe that 9 is a boundary." Also, yes, 0.9 is not equal to 1, nor is 9 equal to 10, but 9 and 0.9 aren't "normal subgroups" of anything. A normal subgroup is a type of subgroup, which is in turn a subset of a group that is also a group. 0.9 and 9 aren't groups.
In abstract algebra, a normal subgroup (also known as a invaariant suibgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation by members of the group of which it is a part. In other words,a subgroup N of the group G is normal in Gif and only if gng ^ -1 element (∈) N for all g element (∈ )G and n element ( ∈ )theusual notation for this relation is N normal subgroup (⪦ )G
All subgroups of the real numbers are normal, so I don't see this as relevant. This is in fact true of any Abelian group. (A group that satisfies the communatative property.)
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@zedvictor4
And I easily demonstrated that 0.9... will always fall .1 or .01 etcetera, short of 1.No rigour required.
You demonstrated that 0.99999... falls short of 1 for finitely many nines. I believe I have already clarified that I am referring to 0.99999... with infinitely many nines. Please explain how you would demonstrate that that falls short of 1.
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@b9_ntt
The fact that the set of all integers contains more terms than the set of all even or odd integers renders the word more (or greater than) meaningless.
These sets are all, rather counterintuitively, the same size. There are, however, sets that are bigger. This video explains it better than I ever could.
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@Math_Enthusiast
#27
There is no error involved, so I don't see this as relevant. You may claim that 0.99999.. = 1 is dependent on error, but that is simply false. I demonstrated in post #14 that this follows from the definition of an infinite decimal.
The error here is the choice in numerical decimal systemthat creates the 0.9999... in the first place. This is not the only error in mathematics,or the only location is a string of formula where error occurs. In post #14 we established only that 0.9, 0.99, 0.999, 0.9999, etc. are groups of subsets of #1 not that they had been precise. We are also describing the use of duodecimal system to negate fractions decimals like (0.9, 0.6, and 0.3).
The Archimedean property states that if x is a real number there exists some natural number n such that n > x, so the Archimedean property has nothing to do with subsets or normal subgroups, nor does it "describe that 9 is a boundary." Also, yes, 0.9 is not equal to 1, nor is 9 equal to 10, but 9 and 0.9 aren't "normal subgroups" of anything. A normal subgroup is a type of subgroup, which is in turn a subset of a group that is also a group. 0.9 and 9 aren't groups.
I respectfully disagree on what is stated as the Archimedean Property uses the symbol ∈ describing a membership betweenreal numbers the letter ( a ) can describing in calculus a value which is fixed and the { } brackets identify a set. meaning group, the group is clearly marked as a subset of 1.0 it is in no way infinite. It is the error translation of decimal which creates the idea of infinite. We might as well just blame the person who invented the calculator for not adding a fraction / duodecimal switch on the device. 9 - 0.9999... are part of the fractional subgroup. Archimedes used the duodecimal system and anticipated calculus to which he dealt with the infinitely small.
All subgroups of the real numbers are normal, so I don't see this as relevant. This is in fact true of any Abelian group. (A group that satisfies the communatative property.)
Some subgroups are Irrational numbers or Natural numbers they are not all "normal." We can compare Time, Degree, Prime, Natural, Irrational, Rational, Odd, Even, etc. and see this.
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@Math_Enthusiast
These sets are all, rather counterintuitively, the same size. There are, however, sets that are bigger. This video explains it better than I ever could.
There is no such thing as a group of people as sets of infinite people infinite describe all the people as one normal group. The bus as explained in the video is stating that a lie is taking place somewhere. If bus (a), being a set value in calculus is in fact infinite there is no bus (b) as set value. Bus (a) is holding all people. otherwise, bus (a) is properly called bus (x) and is an approximation value only.
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@zedvictor4
And I easily demonstrated that 0.9... will always fall .1 or .01 etcetera, short of 1.
No, you didn't.
No rigour required.
It's not complicated, it's just a repeating decimal, so it never falls short. It's just how the decimal system represents a fraction.
1 divided by 3 is 1/3,
1/3 times 3 is 1
1=1 simple
And representing the fractions with decimals is just as simple.
1 divided by 3 is .333...
.333... times 3 is .999...
1=.999... simple.
Sure, the term "infinity" can be very mysterious, but a repeating decimal is just repeating, it doesn't become mysterious because you can think of it as repeating an "infinite" number of times. The repeating "infinity" is not the mysterious infinity, and there's no rigour to it at all.
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@Sidewalker
Nope.
It just doesn't work.
Because you can not divide 1 precisely by 3 decimally.
The equation fails at the first stage.
.3 is 3 tenths
Times 3 = 9 tenths.
9 tenths does not equal 1
Doesn't matter how many 9's.
.999 = 999 thousandths
1 thousandth short of one.
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@zedvictor4
You directed me to post #27:
0.9 = nine tenths.Therefore ten tenths = 1.0.99 = 99 hundredthsTherefore a hundred hundredths = 10.999 = 999 thousandths.Therefore a thousand thousandths = 1And so on.
Here you demonstrate that 0.99999... is not equal to one in the case of finitely many nines. I just clarified that I am referring to 0.99999... with infinitely many nines, yet you fail to address this. I will wait for you to address the case of infinitely many nines.
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@Math_Enthusiast
The problem: There is no step at which you complete the path. No matter how many steps you make, you will never complete the path. The duration of a step is irrelevant, as the step never lasts 0 seconds. Since infinite steps are needed, infinite time is needed as well.
That, my friend, is the math problem.
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@John_C_87
The error here is the choice in numerical decimal systemthat creates the 0.9999... in the first place. This is not the only error in mathematics,or the only location is a string of formula where error occurs. In post #14 we established only that 0.9, 0.99, 0.999, 0.9999, etc. are groups of subsets of #1 not that they had been precise. We are also describing the use of duodecimal system to negate fractions decimals like (0.9, 0.6, and 0.3).
This is indeed a flaw in the decimal system, and it is indeed a human error. This is why mathematicians generally avoid using it. For example, if you ask a mathematician "What is the area of a circle with radius 1?" they will probably not say "3.141592...." Instead, they will probably say "π." You mention the duodecimal system. While it is better, the same issues still remain: 0.BBBBB... = 1 in duodecimal. If you would like to propose a way to avoid this issue, please do. I would love to discuss it.
I respectfully disagree on what is stated as the Archimedean Property uses the symbol ∈ describing a membership betweenreal numbers the letter ( a ) can describing in calculus a value which is fixed and the { } brackets identify a set.
We must be misunderstanding each other here. I agree with this.
meaning group,
Now I understand the issue. "Group" and "set" do not mean the same thing in math: group, set. Please familiarize yourself with these definitions.
Some subgroups are Irrational numbers or Natural numbers they are not all "normal." We can compare Time, Degree, Prime, Natural, Irrational, Rational, Odd, Even, etc. and see this.
I would blame your misunderstanding of the term "group," except that all subsets (subgroup or not) of the real numbers satisfy the defining property of a normal subgroup, so I'm not sure where you are getting this from.
This is the definition provided by you of normal subgroup:
In abstract algebra, a normal subgroup (also known as a invaariant suibgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation by members of the group of which it is a part. In other words,a subgroup N of the group G is normal in Gif and only if gng ^ -1 element (∈) N for all g element (∈ )G and n element ( ∈ )theusual notation for this relation is N normal subgroup (⪦ )G
If S is any subset (not just a subgroup) of the real numbers, then gng^-1 = gg^-1n = n ∈ S by definition of g^-1 and by the commutative property for any n ∈ S and g ∈ G, G here being either the multiplicative group of real numbers, or the additive group of real numbers, whichever you were referring to.
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@Best.Korea
Since infinite steps are needed, infinite time is needed as well.
Thank you for quite nicely spelling out the fallacy in your reasoning: You seem to think that an infinite number of steps cannot be done in an infinite amount of time, as this very example proves.
If logic proves something that is counterintuitive to you, that is probably because you simply find it counterintuitive, and not because the logic is wrong. You haven't actually pointed out a flawed step in my reasoning. Rather, you just declare that the conclusion makes no sense.
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@John_C_87
There is no such thing as a group of people as sets of infinite people infinite describe all the people as one normal group.
This sentence isn't the most readable, but if I'm interpreting it correctly, you are saying that an infinite group of people. That is true. The video is just using something concrete (people) to assist in the explanation. It is not being suggested that any of this could actually happen. Only in the abstract. As the video says, this line of inquiry lead to the invention of the modern cell phone and computer, so if it's all wrong, then I'm not sure how it's possible for us to have this discussion.
The bus as explained in the video is stating that a lie is taking place somewhere.
This is simply false. The video does not make reference to any sort of "lie."
If bus (a), being a set value in calculus is in fact infinite there is no bus (b) as set value. Bus (a) is holding all people. otherwise, bus (a) is properly called bus (x) and is an approximation value only.
Could you please explain what is meant by bus (a), bus (b) and bus (x)?
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@Math_Enthusiast
"I had written."
"I respectfully disagree on what is stated as the Archimedean Property uses the symbol ∈ describing a membership between real numbers the letter ( a ) can describing in calculus a value which is fixed and the { } brackets identify a set."
We must be misunderstanding each other here. I agree with this.
1. We have a membership to group by the use of mathematic"∈" symbol means membership and well it is ArchimedeanProperties we are speak of here.
2. The bracket { } identifythe math principle of set in all math notation not just Archimedean property.
3. Archimedes’ work is on calculus which is in general explanationbrings mathematics of calculus in to describe x as a "little bitof" or most often described as " an element of." The whole ofcalculus describes the topic of element as of being more than on so is sets andgroups of elements.
they will probably not say "3.141592...." Instead, they will probably say "π.
I'm not going to focus on "Pi" as it was part of a list of mistakes to corect. I have always felt this error in desperate needing of a solution. The topic at this point may drive us toa lesser understanding at the moment. On a personal note, I have resolved anyissues with a approximation of Pi, writing a new formulation in trigonometry as theterm cPi using work from Isaac Newton's trigonometry, whereas triangles bothright and left 90 degree angles can be used to calculate circumference as hypotenuseof those respected 90 degree angles. as the letter (c) suggest in calculus Ihave a created a formula that sets a constant that is not irrational as value.
If S is any subset (not just a subgroup) of the real numbers, then gng^-1 = gg^-1n = n ∈ S by definition of g^-1 and by the commutative property for any n ∈ S and g ∈ G, G here being either the multiplicative group of real numbers, or the additive group of real numbers, whichever you were referring to.
so I'm not sure where you are getting this from
In the above exsample did all of the mathematic symbols translate across to this forum.They didn't for me and the math symbols of a triangle with the apex facing right or left is the principle missing for subgroup here.
This sentence isn't the most readable, but if I'm interpreting it correctly, you are saying that an infinite group of people. That is true. The video is just using something concrete (people) to assist in the explanation. It is not being suggested that any of this could actually happen. Only in the abstract. As the video says, this line of inquiry lead to the invention of the modern cell phone and computer, so if it's all wrong, then I'm not sure how it's possible for us to have this discussion.
lol ... yeah it gave me a hard time to write as well. Rephrase, If a infinite number of people on / in one objectis to true. All other buses are empty as fact. There are an infinite number of buses but only one bus of infinite people, as there are no people left to go on any more buses but one. "The whole idea on the video is a lie. Not even a good lie at that." Understand?
Could you please explain what is meant by bus (a), bus (b) and bus (x)?
It is part of a minor math discrepancy about the video. When describing the bus and people in calculus the letters a and b would be written as buses y and z they are variables not fixed values.
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@John_C_87
"I had written.""I respectfully disagree on what is stated as the Archimedean Property uses the symbol ∈ describing a membership between real numbers the letter ( a ) can describing in calculus a value which is fixed and the { } brackets identify a set."
Exactly. { } brackets identify a set, not a group. As I explained, in math, those are two different things. It's an important distinction.
1. We have a membership to group by the use of mathematic"∈" symbol means membership and well it is ArchimedeanProperties we are speak of here.
Yes. Except that the Archimedean property has nothing to do with groups, but rather this symbol is used in the more general context of sets.
Groups and sets are two different things in the context of math. It's really not that hard of a concept.
2. The bracket { } identifythe math principle of set in all math notation not just Archimedean property.
Correct.
3. Archimedes’ work is on calculus which is in general explanationbrings mathematics of calculus in to describe x as a "little bitof" or most often described as " an element of."
Correct.
The whole ofcalculus describes the topic of element as of being more than on so is sets andgroups of elements.
Calculus and group theory really don't have much to do with each other. Especially not the Archimedean property.
Calculus has a lot to do with sets but sets and groups are not the same.
I'm not going to focus on "Pi" as it was part of a list of mistakes to corect. I have always felt this error in desperate needing of a solution. The topic at this point may drive us toa lesser understanding at the moment. On a personal note, I have resolved anyissues with a approximation of Pi, writing a new formulation in trigonometry as theterm cPi using work from Isaac Newton's trigonometry, whereas triangles bothright and left 90 degree angles can be used to calculate circumference as hypotenuseof those respected 90 degree angles. as the letter (c) suggest in calculus Ihave a created a formula that sets a constant that is not irrational as value.
I'm not sure I follow. Are you claiming that the decimal expansion of π is invalid? You reference a formula that you yourself apparently created. Would you care to share this formula in exact mathematical detail?
In the above exsample did all of the mathematic symbols translate across to this forum.They didn't for me and the math symbols of a triangle with the apex facing right or left is the principle missing for subgroup here.
As far as I know, all symbols are appearing as they should.
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@John_C_87
If a infinite number of people on / in one objectis to true. All other buses are empty as fact. There are an infinite number of buses but only one bus of infinite people, as there are no people left to go on any more buses but one. "The whole idea on the video is a lie. Not even a good lie at that." Understand?
There is no reason that there necessarily wouldn't be any people left to ride the other buses. Since this is a hypothetical, we can have as many people involved as we want. If there aren't infinitely many people on every bus, we just add more into our hypothetical. If you would like to demonstrate why it is a mathematical impossibility not to have more than one infinite bus full of people, please present a rigorous proof, rather than simply declaring it as fact.
It is part of a minor math discrepancy about the video. When describing the bus and people in calculus the letters a and b would be written as buses y and z they are variables not fixed values.
Everything in the video has a fixed value. The cardinality of the hotel and of the buses is aleph null, and the cardinality of the party bus at the end of the video is the continuum. (see the second meaning of "continuum" on the linked webpage) Cardinal numbers never show up in calculus, but this isn't calculus, it's set theory.
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@Math_Enthusiast
Yep.
There is a reason for an infinite number of nines.
And I just explained why.
Exactly. { } brackets identify a set, not a group. As I explained, in math, those are two different things. It's an important distinction.
More importantly in calculus a set, and a group of sets are caculated in formula Archimedean Property using the symbol to describe groups, and the symbol for sets of groups. 0.99999 describes 6 groups { 1.0, 0.9 , 0.09, 0.009, 0.00009 } describes 5 groups. We agree the brackets are fractional sets?
"A group is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of closure, associativity, the identity property, and the inverse property. The operation with respect to which a group is defined is often called the "group operation," and a set is said to be a group "under" this operation. Elements , , , ... with binary operation between and denoted form a group if"
1. Closure: If A and B are two elements in G , then the product of A B is also in G.
"A binary operation f (x, y) is an operation that applies to two quantities or expressions x and y .
A binary operation on a nonempty set A is a map f A x A > A such that
1. f is defined for every pair of elements in A , and
2. f uniquely associates each pair of elements in A to some element of A .
Examples of binary operation on A from A x A to A include addition (), subtraction (), multiplication ) and division ()."
A binary operation on a nonempty set A is a map f A x A > A such that
1. f is defined for every pair of elements in A , and
2. f uniquely associates each pair of elements in A to some element of A .
Examples of binary operation on A from A x A to A include addition (), subtraction (), multiplication ) and division ()."
Everything in the video has a fixed value. The cardinality of the hotel and of the buses is aleph null, and the cardinality of the party bus at the end of the video is the continuum. (see the second meaning of "continuum" on the linked webpage) Cardinal numbers never show up in calculus, but this isn't calculus, it's set theory.
Infinite people, infinite buses, infinite rooms, andinfinite hotels...Are to be proven that is the Hypothesis. The groups ofpeople on the bus do not end, nor do the groups of rooms in the hotels. The veyuse of odd even rooms in the video, the people on the buses are all still allpeople, simply the infinite group is on every bus to be counted in simultaneoussequence.
I'm not sure I follow. Are you claiming that the decimal expansion of π is invalid?
Yes.......no, mathematics states Pi is invalid.
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@zedvictor4
Nope.
Yep
It just doesn't work.
Yes it does
Because you can not divide 1 precisely by 3 decimally.
Of course you can, so one divided by three times three equals one with fractions but not with decimals? You show that when the decimal is not repeating it doesn't work, but so what, the decimal is repeating. Are you challenging the validity of the decimal system because you disapprove of repeating decimals, really?
The equation fails at the first stage.
At the stage where the decimal isn't repeating, so what?
.3 is 3 tenthsTimes 3 = 9 tenths.9 tenths does not equal 1Doesn't matter how many 9's..999 = 999 thousandths1 thousandth short of one.
Yep, when the decimal is not repeating it doesn't, but so what, that has nothing to do with it. There is no point at wheich a repeating decimal halts, that's like saying the number of natural numbers is not infinite, it must be finite because at some point you stop counting.
You can't just inject rules into mathematics because the word "infinite" has to be mysterious.
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@Best.Korea
The problem: There is no step at which you complete the path. No matter how many steps you make, you will never complete the path. The duration of a step is irrelevant, as the step never lasts 0 seconds. Since infinite steps are needed, infinite time is needed as well.That, my friend, is the math problem.
You discount the fact that you prove yourself wrong a thousand times a day, every day. According to you, movement is impossible, presumably you can actually move, how do you explain that?