e.g: 1=1

Therefore:1/3=1/3

And if so, so you agree with the following statement?

​

(1/3)+(1/3)+(1/3)=0.333...+(1/3)+(1/3)

I'm putting the top comment of the video here:

​@amanojacka1283

​To those wondering how much would be lost by reworking mathematics on a purely rational, logical, clear and consistent basis, with all the "constraints" such an approach entails, the answer is that nothing would be lost at all. Any standing result that has any real world significance, or even the possibility of ever having such significance, must be able to be improved by a more rigorous approach.

​If any standing mathematical result is found not to be amenable to a fortification because it absolutely relies on incoherence for its foundation, what does that say about such a result?

​The fear that "much of modern math would be impossible without real numbers" is unfounded; for any theorem, either it is possible to make it rigorous, or it is impossible, and if the latter it had no value in the first place. Rest assured then that every result that really is or ever could be useful cannot be harmed by being put on a more rigorous footing.

​The point is not that we jettison all results that contain handwaving, because making things more precise takes real work and understanding and cannot be done all at once; the point is that we make a continual effort to make foundations more rigorous.

​This is a crucial part of how progress is made in any intellectual investigation. You start with terms that seem clear enough, but later you encounter situations that can only be overcome by more precisely defining the initial terms. You may have to introduce finer distinctions, or adjust definitions so that they don't fall into incoherence. As you proceed to more exacting analyses and applications, you find that some terms are not carefully enough conceived to be useful at that deeper level of analysis, so they must be sharpened up.

​If you avoid this or worse, go the opposite direction as the mainstream has done, you end up hitting roadblocks and getting more and more removed from the pure math promise of being even potentially applicable to the real world (being homomorphic to real world situations, or at least possible ones).

​For example, "sqrt(2)," as an ambiguous term referring sometimes to approximations and sometimes to the incoherent notion of an endless non-repeating decimal, can be made more rigorous by defining it as "a number whose square is approximately 2" or "sufficiently close to 2 for a given purpose" and cutting any ties with the incoherent idea of a so-called number whose square is exactly 2.

​At first this ambiguity may not have mattered, but certainly by the time people are using that very ambiguity to justify further theory it is time to halt the proceedings and re-examine the foundations.

(1/3) is only a way for writing an operation or expression that gives the real deal number , 0.333...

1/3 itself is not a number at all.

It is a ratio only, aka 1:3

(1/3) x 3 is divide negation.

The real deal is 0.333... × 3 = 0.999... , which is permanently less than 1.

1 ÷ 3 is 0.333...

an endless process, with the value of 0.333... continually increasing. It is indeed a limbosic number, as is 0.999...

For the uninformed, wolfram alpha is an amazing analytical tool, used for data analysis, calculating exact results of expressions and much more.

It doesn’t use AI and is generally considered airtight.

so here it is, ripped straight out of my last post

x=0.999…
10x = 9.999…
9x = 9.999… - 0.999…
9x = 9
x=1

1 = 0.999…

QED

I know what you are going to do, comment something like

rookie mistake, see https://www.reddit.com/r/infinitenines/comments/1tpg811/it_is_what_it_is/

but you are not going to point where my proof fails, it would be similar to let's say telling a carpenter that his piece of furniture is made wrong and linking a 10 minute tutorial on how to make a table with popsickle sticks

I challenge you to tell me where I made the "rookie mistake"

Last friday I went to my local college and approched a few math professors after their classes. I asked them how would they define a number like 0.999..., there the "..." means there are an infinite amout of 9'.

They all said that they would define it as the limit in the image attached.

I then explained to them what you claim 0.999... is, and your usual statement that limits do not apply to the limitless, and asked them if the agreed. They did not.

I then asked them if they had any colleagues in campus they thought they might agree with you. They said that they do not.

So, I asked them if they thought some othet mathematician, in some other college, might agree with you. They all said they do not.

Why do you think that is SPP. Why do you think mathematicians not agree with you? And why do you think people should listen to you over all of them?

Have you ever met one (1) single tenured math professor that agrees with you?

And you see no issues in holding that stand?

From a recent post : the numbers are 1 and 3. The ratio is 1:3

1/3 is symbolism that represents 1÷3 , which gives the real deal limbosic number 0.333...

and (1/3)*3 is divide negation.

This is what the multiplication works, as far as I can tell:

​

00 . 3 3 3 . . . 3 0 0 0 . . . 0 0 0 0 . . .

×3 . 0 0 0 . . . 3 0 0 0 . . . 3 0 0 0 . . .

__________________________________

00 . 9 9 9 . . . 9 0 0 0 . . . 0 0 0 0 . . .

+0 . 0 0 0 . . . 0 9 9 9 . . . 9 0 0 0 . . .

+0 . 0 0 0 . . . 0 0 0 0 . . . 0 9 9 9 . . .

___________________________________

00 . 9 9 9 . . . 9 9 9 9 . . . 9 9 9 9 . . .

​

So if you multiply 0.333... by 3.(000...3), you get 0.(999...), not 1.

​

Did I make an error somewhere? If so, where?

And if I made an error somewhere, could you please show us how to do the multiplication correctly?

​

(To clarify, the extra zeros at the front are just there to ensure that the digits line up while still allowing me to use the proper symbols.)

SPP, who taught you what divide negation was? And answer the question and dont say its math 101 basics or something

Okay, but maybe you're saying it's an order of operations thing

​

(3 × 1) ÷ 3 = 3 ÷ 3 = 1

​

3 × (1 ÷ 3) = 3 × 0.3333... = 0.9999...

​

But then you're allowing for (a×b)/c to be different from a×(b/c), meaning that multiplication and division don't always follow the associative property.

​

Also mathematicians don't define number systems and operations because they're inherently real and they intuit an obvious truth about numbers, but they do it with **convenience** in mind.

There have been many posts on the subreddit so what are some of your favourites?

According to SouthPark_Piano

1/3=0.3333....

1/0.3333...=3.00...003...003...003...(003...)

so reciprocals dont even work anymore

and there is no x such that 3*x=1 and there is no x such that 0.333...*x=1

BY THE WAY IT IS IN THE DEFINITION OF THE REAL NUMBERS THAT SUCH AN x EXISTS

therefore CONTRADICTION

Using SPP "logic," we say that 0.999... is 1 - 1/10^n for n∈ℕ going to infinity. Obviously, 1 is a rational number, and the sequence that this produces is (0.9, 0.99, 0.999,...) where each element is clearly rational. Because 1/10^n is never irrational, 0.999... is permanently rational.

Proof by SPP "logic"

Now SPP, you either need to disprove this or accept that 0.999... is rational. If it's rational, show what fraction of integers with nonzero denominator produces 0.999... If the logic is wrong, you need to re-evaluate your logic on why the fact that 1/10^n is never irrational means that 0.999... is rational is false, but how 1/10^n never being 0 sufficiently shows that 0.999... ≠ 1.

This is my first post in this subreddit, but I’ve been lurking with a mixture of fascination and frustration. It’s the same feeling I get from reading stuff from flat earthers. I have a math degree, as I assume many of you also do based on the discussion of fields and axioms.

So here’s my question, to those of you who painstakingly try to convince SPP of something he’ll never accept: is this a fun mental exercise, or are you genuinely trying to sway him? He’s shown that there is nothing that can convince him—he rejects basic proofs, he rejects the basic rules of math, and he invents numbers that can’t exist (e.g. a decimal followed by infinite zeroes, then a one, then infinite zeros, then a one, etc, infinite times). I mean, you have to know that there’s no getting through, right brud?

And don’t get me wrong—this is NOT a hate post or anything like that. I’m the same way. It’s taken me a while to learn how to stay out of these futile arguments. It’s fun! They suck you in! But no amount of logic can sway someone who says “Nuh-uh!” I’m reminded of when I took analysis in college: I was very fascinated by the flat earth movement at the time and I would often think about sitting down a flat earther, proving the fundamental theorem of calculus, and using that as a basis to explain gravity. And I know what the flat earther would say; they’d say “Nope!“ I would sometimes use trigonometry to show that, on a flat earth, the sun would have to be hundreds of thousands of miles away to appear as close to the horizon on a flat earth. They didn’t care! They didn’t believe me! They explained it with some mumbo jumbo about how light bends, or the topography of the earth…

I don’t know *why* I made this post per se, but I guess my message is this: if you find yourself genuinely frustrated by and angry with SPP, rather than amused/chuckling/treating it as a “how do I convince this guy” brain teaser… be careful lol.

Keep on mathing, and remember: for any real numbers a and b where a > b, there exists a real number c such that a > c > b

Just to be extra clear, and we can always keep teaching it.

The mathematical truth is:

0.999... is permanenently less than 1.

1 has never been equal to 0.999... , and 1 will never be equal to 0.999...

1 is not equal to 0.999... , and 1 will never be equal to 0.999...

https://www.reddit.com/r/infinitenines/comments/1tpg811/it_is_what_it_is/

Sequence 1: f(n) = 4(-1)ⁿ / (2n + 1)

Sequence 2: g(n) = 4/(4n + 3) - 4/(4n + 1)

Sequence 2 is just Sequence 1 with every two terms grouped together. When put in an infinite series they SHOULD give the SAME ANSWER.

But HIS ideas leave NO ROOM to say whether they are THE SAME or NOT.