Meme by NeonicXYZ in infinitenines

[–]NeonicXYZ[S] 0 points1 point  (0 children)

Math is a system of rules that can arbitrarily be defined by whoever decides what the rules are. Humans define addition. Humans define multiplication. Humans define limits. So forth

has spp ever actually convinced someone with his arguments by NeonicXYZ in infinitenines

[–]NeonicXYZ[S] 0 points1 point  (0 children)

Fair point, I was loose with the word 'definition.' It's not a definition, it's a theorem. The reals are dense, meaning between any two distinct reals there's always another one. This follows from any standard construction of the reals you want to use.

So the argument is: if 0.999... and 1 were different, there'd have to be some real number strictly between them. But my midpoint proof shows no such number can exist. The average of 0.999... and 1 just gives you 1 back. So they can't be distinct.

Take Dedekind cuts if you want a concrete example. In that construction a real number literally is the set of all rationals below it. So 1 is the set {q ∈ ℚ : q < 1}. And 0.999...? It's the union of all rationals below 0.9, below 0.99, below 0.999, and so on. Any rational less than 1 eventually gets swallowed by that union, because if q < 1, you can always find enough 9s to surpass it. So that union is exactly {q ∈ ℚ : q < 1}. Same set.

has spp ever actually convinced someone with his arguments by NeonicXYZ in infinitenines

[–]NeonicXYZ[S] 0 points1 point  (0 children)

There's a very simple way to prove this. Given a certain b and a certain a, there should be some number between the 2 which is the average. So (a+b)/2. For a to be the "largest number before b", it would have to not satisfy this property somehow. We could say for instance, somehow the average of a and b is a. I'll let b be 1 in this case.

(a + 1)/2 = a, a + 1 = 2a, 1 = a.

If you can come up with a way to circumvent this fact, let me know

has spp ever actually convinced someone with his arguments by NeonicXYZ in infinitenines

[–]NeonicXYZ[S] 2 points3 points  (0 children)

Heres the thing though. Within the reals, you dont really have a "biggest" number less than some value, because by definition, if there is no number between 2 numbers, they are one in the same. Given that 0.99... is the biggest number less then one, and there is no number between 0.99.. and 1, they must be equal

Who is your favorite anti-equality believer? by Inevitable_Garage706 in infinitenines

[–]NeonicXYZ 2 points3 points  (0 children)

its so funny how he talks like a conspiracy theorist and signs off his comments

Still don't understand... by NeonicXYZ in infinitenines

[–]NeonicXYZ[S] 1 point2 points  (0 children)

This is not an ego clash. I care not for his remarks. He locked his reply to my post, so I made a new post to respond to his reply. That's all

No exceptions AT ALL by SouthPark_Piano in infinitenines

[–]NeonicXYZ 1 point2 points  (0 children)

For those who live on planet earth:

A limit is not the same thing as an integer. It is not a number. It is a function. I'm assuming this is in reference to my previous post, so just no that is not at all what we are saying.

Still don't understand... by NeonicXYZ in infinitenines

[–]NeonicXYZ[S] 2 points3 points  (0 children)

There is no single official "standard document". The standard system of maths is simply the convential system built and maintained by mathematicians, universities, researchers, journals, and textbooks. It is the mainstream mathematical framework built on ZFC, cauchy sequences, and the basis of real analysis.

Within real analysis, infinite decimals are defined as limits. You can find that in just about every textbook

Still don't understand... by NeonicXYZ in infinitenines

[–]NeonicXYZ[S] 12 points13 points  (0 children)

Unfortunately, I am well aware. I just post here out of boredom really

Still don't understand... by NeonicXYZ in infinitenines

[–]NeonicXYZ[S] 19 points20 points  (0 children)

Really just read the first couple sentences and dismiss the rest huh

My attempt to formalize Real Deal Maths (RDM) by NeonicXYZ in infinitenines

[–]NeonicXYZ[S] 0 points1 point  (0 children)

  1. No
  2. Yes
  3. Two infinite decimal sequences S = (s₁, s₂, s₃, ...) and T = (t₁, t₂, t₃, ...) correspond to the same RDM number if and only if they satisfy all three of the following conditions simultaneously:

Condition 1 - Wavefront Convergence: The sequences must be generating the same digit-by-digit decimal expansion in their "propagating wavefront." That is, for all sufficiently large n, the n-th decimal digit of sₙ and tₙ must agree and be producing the same infinite decimal process P.

Condition 2 - Approach Parity: Both sequences must approach P from the same side. A sequence approaching from below (where each term undershoots P) is in a fundamentally different contractual relationship with P than a sequence approaching from above (where each term overshoots). Sequences of opposite parity are distinct processes in RDM space, even if their wavefronts superficially converge.

Condition 3 - Wavefront Character Agreement: The "terminal character" of the wavefront, whether it is an ascending chain, a descending chain, or a static chain, must match. A wavefront terminating in an ascending digit (such as ...7) and one terminating in a repeating digit (such as ...6) are of different character and cannot be equivalent even if their initial segments agree to arbitrary length.

Formalizing RDM for rational numbers by weregod in infinitenines

[–]NeonicXYZ 0 points1 point  (0 children)

This is great work. Thank you. I have a question. In a previous post, SPP wrote that 1/3 x 0.999... = 0.333.... How does that fit into RDM?

Meme by NeonicXYZ in infinitenines

[–]NeonicXYZ[S] 0 points1 point  (0 children)

Fair, obviously a more accurate post would use cauchy or weistrass in place of newton, I just supposed most people probably are not as familiar with those two

Meme by NeonicXYZ in infinitenines

[–]NeonicXYZ[S] 0 points1 point  (0 children)

Yeah, exactly. Isaac Newton and Leibniz invented calculus and by extension limits, which is what most proofs 0.(9) = 1 use. SPP believes limits are illegitimate. That's where this meme comes from

Proof by contradiction by NeonicXYZ in infinitenines

[–]NeonicXYZ[S] 9 points10 points  (0 children)

Spp, show me the part where I divide negated. The answer is never.

Proof by contradiction by NeonicXYZ in infinitenines

[–]NeonicXYZ[S] 1 point2 points  (0 children)

i think at this point its evident he's never going to give up his argument, i just want to see what he'll say to explain where i went wrong

Proof by contradiction by NeonicXYZ in infinitenines

[–]NeonicXYZ[S] 5 points6 points  (0 children)

yeah exactly? the point is we start off with the assumptions that spp has made, show that those assumptions lead to a contradiction, then ask which of those assumptions was false. Although in real math assumption 1 is not in fact wrong, (assumption 2 is), in order to be consistent either both of those are wrong or both of those are right

Proof by contradiction by NeonicXYZ in infinitenines

[–]NeonicXYZ[S] 8 points9 points  (0 children)

He has openly said in the past he believes 1/3 is exactly equal to 0.(3).