Why the repost? Also plz check my reply in the original post.

Ah got it. This is about your comment from the other one. My bad.

Any chance you could take a look at my comment regarding the factoring problem with your math?

Thanks! I'm really just curious how you got between those two steps. It's actually the same issue in this one so feel to reply in either place

No problem, just wanted to figure out the math myself! Thank you for putting reason before ego.

Lol

0.000.... recurring, or ∞

No.

I don't know what kind of evidence you want that 0 doesn't equal infinity. I suppose a dictionary? That just isn't what infinity means. You can say it has an infinite amount of potential digits right of the decimal, but that's different than equaling infinity.

What is the limit of 1/x as x goes to infinity....

At least most intro to calc books I've seen seem to agree it's not infinity

elaborate

1 = ∞ because 1 is actually 1.0000∞

lol

Also ∞ - ∞ doesnt equal ∞ it would equal 0

You also have several divide by zero errors in your maths.

Also ∞ - ∞ doesnt equal ∞ it would equal 0

I don't think this is true. ∞ - ∞ is typically said to be indeterminate. http://mathworld.wolfram.com/Indeterminate .

Indeterminate is often used to talk about these, but not correct. Things like 0/0 and infinity minus infinity are simply undefined when it comes to standard math.

An indeterminate form always refers to a limit of function that we can write in terms of other functions that would normally allow us to use continuity to just plug in the value, but is undefined when we plug in the value so it's value is not clear.

I came here expecting just one. I was pleased to see that gift to just keep on giving.

This proves math is a tool, not the truth.

zero is a real number, infinity is not a number, therefore zero is not infinity QED

You’re saying “0 = infinity” where at best you could afford saying it’s = 1/infinity

Elaborate as in "is this post an elaborate parody"?

You are not even wrong.

The factoring problem is in this one too. Same issue as last time.

I still remember when I took Advanced Calculus, using geometric series and algebraic factoring to get formulas that could be used to show any number equal to any other number. But then to jump from that to stating it is mathematical proof of a quantum simulation is um...a little bit of stretch?

We should also be able to show the inverse mathematically. So what conditions would need to exist for us to be able to prove we are not in a quantum simulation? The way I read your logic is the only way to be outside of the simulation is if mathematics doesn't exist.

So a simplified version of the proof is: 2+2=4 proves we are in a quantum simulation. My math is solid but my conclusion might be a tad off.

I own you an apology. On your last thread regarding flat earth I was sure you were trolling. Kudos to you for trying to find answers, even if you are criminal wrong on some parts.

You exhibit a problem that alot of people do: not understanding mathematics. I don't talk about being able to solve algebra or calculus (the second part also something I would suggest most people including you can't do), but rather understanding what numbers and mathematics are.

For example, this line:

a x (b - a) = 1 x (1 - 1) = 1 x 0 = 0 (to be correct 0.000.... recurring, or ∞) makes absolutely zero sense. How can a number be equal infinity? A number can has infinite number of digits, or can be displayed as a number with infinite digits, but where the equality comes from?

If you want I can screen cap your thread, highlight everything that is wrong, write why its wrong on the margin (for example, Intermediate Form, for your ∞ - ∞ = ∞ belief), and sent it to you so you can refresh on the problems and re-evaluate your conclusions.
Or, if you have any questions regarding the maths you use (ie, why you, as a rule, can't divide by zero), let me know.

why you can't divide by zero Maybe this example will help give you a more intuitive understanding of division by zero.

-2/1 = 2 -2/0.5 = 4 -2/0.25 = 8

We notice a trend here; as the denominator (bottom number, the number we are dividing by) get smaller, the answer becomes larger. We keep letting the denominator get smaller until we get to zero, what happens at zero? First let's rearrange these fractions by multiplying the answer by the denominator.

-2=2x1 -2=4x0.5 -2=8x0.25

Now we'll think about it in terms of money. If I have dollar coins, I need two dollar coins to have two dollars. If I have a fifty-cent coins, I need four of them to have two dollars. If I have quarters, I need eight of them to have two dollars. If I have zero cent coins, how many would I need to have two dollars?

There are no amount of zero cent coins that would get me to two dollars, because no matter how many of them I have, they are all still worth zero dollars. So the answer is that there is no number of zero dollar coins that will get me to two dollars. If you rearrange this (2 =\= (0 dollar coin)x(any number of zero dollar coins)) back into a fraction, you see the answer is essentially that there is no answer.

For a more formal explanation, let's look at the expression "2/X". We want X to keep getting smaller and smaller, getting ever closer to zero. This is the mathematical concept of a "limit". Formally, we would ask what the limit of 2/X is, as X approaches zero. The answer to this question is infinity.

However, there is an important distinction to be made here. The limit of 2/X as X approaches zero is infinity (but we never let X actually equal zero!), but the expression 2/0 does not equal infinity.

0.00000... = infinity There may be infinitely many digits in this number, but that is not that same as having a value of infinity. If I have $3.50000..., I certainly don't have an infinite amount of money!

To add onto this, whether 2/x approaches positive infinity depends on whether you approach 0 from the positive or negative direction.

Because the limit approaches two different values depending on where you approach it from, the limit is said to not exist.

why can I not logic it out?

Assume a normal mathematical expression a / b = c . Any values you put into that must also satisfy the equation a = b * c since all we've done is divide by b on both sides. If you assume b = 0 and a ≠ 0 , then you cannot solve for c, because you end up with e.g. 1 / 0 = c which is required to equate to 1 = 0 * c by the simple rules of algebra. The problem is there is no number c which you can multiply by 0 to get 1 , therefore, dividing by zero simply can't be done.

two goes into zero infinity times.

You misspelled insanity as infinity. Two doesn't go into zero even once, let alone an infinite number of times.

0.0000etc the same as zero

To illustrate just how absurd this suggestion is, consider that by your own definition, of 0.0 has an infinite number of 0's, making it equal to infinity. However, if infinity = 0, then it actually has 0 trailing 0's, and your problem is resolved. The rest of your points depend on this not being the case, but it is, so they don't need addressed except for one.

is 0.9999 recurring the same as 1

Of course it is. The fact that you don't believe this is probably why you invented this nonsense in the previous point, so let me explain perhaps differently than you've heard of before. The error comes in when you insist on representing 1/3 as a decimal. It cannot be accurately represented this way simply because 3 is a prime that is not a prime factor of 10, the base we are working in.

If you switch to base-6, base-30, or any other base that has 3 as a prime factor, then 1/3 divides out cleanly with no repeating digits.

The only prime factors in base-10 are 2 and 5. Dividing any number by any other number will result in an infinite decimal representation if there is a prime in the denominator that is not also in 2, 5, or the numerator.

The repeating decimals you get from division are not "real". They are purely an artifact of the base you are doing your calculations in.

Suggesting otherwise is as silly as suggesting that 1/3*3 ≠ 1 .

Hello!

The first three of your points tackle the same problem, division by zero, so I will try and explain them at the same time, if that's ok with you. If not, please point to your objection and I will delve further into it:

Division is the operation by which a set is fully partitioned into a number of subsets, resulting in each subset containing the same info. 10 apples are "split" into 5 persons, resulting into 2 apples per person. All persons have been give the exact number of apples and no apples are left over (keep in mind that we do not care if it's a whole or 1/3 of an apple, we only care that there is nothing left and everyone got the same). On your Schoolyard example, you have two problems:

First of all, do you have apples left over after you split them up? if so, you did the operation wrong. I am sure if we were splitting money and 100 dollar were "left over", you would argue that we didn't split them correctly. Can you find a result where you split the apples evenly against the person and no apples are left over? Secondly, how many subsets you have before the operation? Zero. How can you have "split" something if you can't "award" it to a subset in the first place? You simply cannot do it, can you? You physically cannot do the division of 2 apples to zero persons. You wouldn't know where to start.

Those two points make it impossible to accurately define what would happen if you divide something by zero. Compare your example of 2 apples to zero persons by another one with different numbers, so you can see that the new example answers both points accurately. Furthermore, compare it to a division where the numerator is 0, for example 0 apples split into 5 persons. Has everyone received the same amount of apples? Yes. Do I have apples left over? No. Has there been a number of "entities" where I tried to split the apples onto? Yes. Therefore, the problem only exists when zero is the denominator. On the infinity question. Two does not go into zero infinite times. It goes in an undefined number of times. If you have two dollars and you have to split them to your 0 kids, do you suddenly have infinite money? You could argue that your kids have infinite money, but can you point to a kid (a subset) that has infinite money (a partition of the original set)?

Regarding recurring numbers: You are correct that 0.00.. is the same as 0, and 0.999... is the same as 1. Keep in mind they are not "almost 0 / almost 1". They are exactly equal to 0 or 1 in their respective cases. It is just another way or writing the numbers, just like 0/1 can be used instead of zero and 3/3 or 1.00... is another way of writing 1. A number can contain infinite number of information (for example, digits), but not be infinite itself. π for example, contains infinite digits but its not infinite itself, is it? its 3.14159... 3.15 is larger than π. Would you argue that 3.15 is larger than infinity?

To conclude, I believe that you are mostly confused with infinity. I mean no disrespect, it is an EXTREMELY common subject for people to get confused into. Some people, for example, believe that you can have things like 1.88...9, which is impossible. If you had a 9 at the end, you can't have infinite 8s before it, can you? Some things like ∞ / ∞ are intermediate forms that touch on infinity being both a number and a concept and the fact that not all infinities are the same "size". Those are beyond the scope of this discussion. I would suggest thinking of infinity as "the largest number I can think of". It will serve you for 99.9% of your everyday life. On your stated examples, is 0.00... the largest number you can think of? No? Therefore is not infinity.

Looking forward to any questions.

why can I not logic it out? ie, schoolyard division, 2 / 0 ; there are two apples, divide them between zero people, how many apples does each person get? zero.

If there are 2 apples, 2 people, and everyone gets 0 apples then there are still 2 apples in the pile, meaning 2/2 =/= 0.

If there are 2 apples, 1 person, and everyone gets 0 apples, then there are still 2 apples in the pile, meaning 2/1 =/=0

If there are 2 apples, 0 people, and everyone gets 0 apples, then there are still 2 apples in the pile, meaning 2/0 =/=0

why can I not logic it out? ie, schoolyard division, 2 / 0 ; there are two apples, divide them between zero people, how many apples does each person get? zero

Perhaps 2/0 = 0, lets examine that situation:

If you have 2 apples in a pile, and divide them among 0 people, then everyone gets 0 apples, and there are 2 left over: 2 - (2/0) 0 = 2 - 0 0 = 2

If you have 2 apples in a pile, and divide them among n people, then everyone gets 2/n apples, and if n =/= 0 there are 0 left over: 2 - (2/n)*n = 2 - 2 = 0

However what if you have 2 apples in a pile, and divide them among 0 people, then everyone gets 1 apples, and there are 2 left over: 2 - (2/0) 0 = 2 - 1 0 = 2

Choosing 2/0 = 0 was arbitrary, choosing 2/0 = 1 was arbitrary. We were both equally justified in our decision of the value of 2/0, because neither of us has any justification for our choice beyond "it looks nice". There are some justifications for having 0/0 be equal to 1 for some theorems in combinatorics, but thats because its usually shorthand for saying "yeah I know this can be 0/0, and for that case there's only 1 thing to count".

obviously, why you can't divide by zero

Formally division is just multiplication by the inverse. So a/b is a time the inverse of b. But this raises the question, what does the inverse mean? Well the inverse of a number x is (if it exists) the number y such that

xy = 1

If there are no such y, then x is not invertible.

It can be proven that there is no real number y such that 0*y = 1, and so 0 is not invertible.

So many things wrong with this.

Zero is not an irrational number (it is a whole number). Infinity is not an irrational number, and should not in general be treated as a number at all. Zero does not equal infinity (you can't just define something like that arbitrarily).

You also seem to have a loose grasp on what a qubit is and how it is used to do calculations. You should read more about them before using them in a "proof" like this.

let's press on with our plan to lift the curtain on the fabric of reality and look deeply into the essence of existence

lol. no.

you are obviously someone who hasn't studied mathematics. no offence but... it's very obvious that your math logic is lacking.

you've made several silly equalities here.

You define a=b=1 in the beginning and then come to conclusion that 0=1. This means you made at least one mistake. Math is never self contradictory. Cardnality

Non-Mobile link: https://en.wikipedia.org/wiki/Cardinality

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Wouldn't the fact that there are just as many numbers between 0 and 1 (infinite) as there are between 0 and infinity be self contradictory?

Yes until you understand some set theory. Specifically cardnality. See above link.

Yes I did check the link b4 asking. But isn't set theory just a convenient way of ignoring the contradictory nature of infinity?

Look up the axiom of choice. That is what set theory hinges on. There is debate as to whether it is corect or not. In this case we are talking about the size of said interval. Using the axiom of choice you can prove that both of your intervals are the same size. Some infinities are bigger than others however. Like I said you have to assume the axiom of choice is correct. At work sorry for the choppy responce.

Thank you for the response. Looks like I have some research to do.

I guess it just bothers me that our math is not perfect even though the way math works it should be. How are we supposed to understand the universe around us when we can't even solve for pi? I use a lot of trigonometry in my work and it's funny that even the most accurate of measurements are just close enough's.

Math giving us results we don't like isn't the same as math being imperfect. It turns out that pi has an infinite decimal expansion. This is inconvenient for us, but it does not mean mathematics.

Also, the commenter above is incorrect - set theory does not rely on the axiom of choice. If you want to learn about set theory, I would recommend Elements of Set Theory by Enderton. It can get technical, but even if you only read the start of the book it will give you a good idea of why set theory was formulated the way it was, and how results in it are found. It even delves into some philosophy of math and infinities, since that seems of interest to you.

math is perfect, your intuition is the imperfection

and we can solve for pi up to an arbitrary number of digits, if you're complaining that we can't store an infinite amount of information then you may want to rethink that perspective

This is not true. You do not need the axiom of choice for either of those things, and set theory does not hinge on it at all. A large subset of set theoretic results, including major systems like Peano arithmetic, do not rely on the axiom of choice.

You're right. I haven't really thought about these things in years. I'm a physics guy. However it's is my understanding that to make a bijection from one infinite set to another you so need the axiom of choice. Isn't that what is happening when mapping (minus infinity, infinity) to the open interval (0,1)? What am I getting wrong here?

Nope, you just make the bijection.

The axiom of choice states that when you have a set of non-empty sets, you can construct a new set by taking one element from each of those non-empty sets. In particular, it states that you can do this even when your set of sets is uncountable. This allows you to create some very paradoxical constructions, partly because makes non-measurable sets out of measurable sets, and partly because the construction is not explicit so it 'feels' wrong.

However, in making the bijection, we do not such construction, and we are not creating any set, we are just matching up elements of two sets.

Wouldn't the fact that there are just as many numbers between 0 and 1 (infinite) as there are between 0 and infinity be self contradictory?

It comes down to what you mean by "as many." In daily life when we want to determine whether there are "as many" things in one set as there are in another, we do that by counting those things. More precisely, for each set we pair up every element in that set with a unique natural (counting) number starting at 1. We continue that until every element has been paired up, and then we compare the highest number we got to for each set. But if both sets are without end, that doesn't work.

Cardinality is kind of a variation of our daily, intuitive notion of size, that extends to sets with infinitely many elements. It does this by skipping the part where you pair up elements with numbers, and just tries to pair up elements form one set directly with elements from the other set. Two sets have the same cardinality if (in principle) you could uniquely pair up each element from the first set with one element of the second set without leaving any unpaired.

Long story short, this is not a contradiction because "size" is not the same thing as cardinality.

Why is a=∞ and b=1, when a=b? Shouldn't they both be the same value? So it's not 1 that equals 0,1,2,∞; it's a = {0, 1, 2, ∞} and b = {0, 1, 2, ∞}, right?

Hahaha you're definitely not a math person.

0.000 recurring doesn't equal infinity. You also can't divide by zero, which you do based upon your own definition of a=b. Not to mention you can't just use infinity as a number in an equation. In calculus you can have limits that approach infinity, but you can't start using it like that.

I hope nobody reading your post thinks you know what you're talking about

I don't mean to sound rude, but you seem to have some fundamental misunderstandings about mathematics. An irrational number is a real number which cannot be expressed as the ratio of two whole numbers. By this definition 0 is clearly rational since it can be expressed as the ratio 0/1 (or 0/2, 0/3, ...). Furthermore infinity is not a number at all, it is a concept. I suspect that part of your confusion may lie in the fact that the decimal expansion of 0 contains infinitely many 0 digits. But this does not make 0 equal to infinity.

Where does this a = b + a come from? It doesn't follow from the previous statement:

a(b - a) = (b + a)(b - a)

You cannot divide both sides by (b - a) because b - a = 0. You are getting undefined behavior when you do this. If we substitute your values in, we see that that statement is merely 1 * 0 = 2 * 0. I think you can see where the issue lies. I do applaud you for being interested in proofs and working things out on your own however. You should definitely look into something like Khan Academy or OpenCourseWare to learn more; you would probably find it interesting.

a(b-a) = (b + a)(b-1) cannot be reduced as (b-a) = 0 and 0 has no multiplicative inverse.

In other words, you cannot divide by zero because that operation is undefined

Yes I did check the link b4 asking. But isn't set theory just a convenient way of ignoring the contradictory nature of infinity?

Nope, you just make the bijection.

The axiom of choice states that when you have a set of non-empty sets, you can construct a new set by taking one element from each of those non-empty sets. In particular, it states that you can do this even when your set of sets is uncountable. This allows you to create some very paradoxical constructions, partly because makes non-measurable sets out of measurable sets, and partly because the construction is not explicit so it 'feels' wrong.

However, in making the bijection, we do not such construction, and we are not creating any set, we are just matching up elements of two sets.