Talk:2956: Number Line Branch

Is it significant that the branch point is close to the value of π? Barmar (talk) 20:28, 8 July 2024 (UTC)

I was thinking the same thing, but decided it was probably nothing worth mentioning - probably just an arbitrary starting point. *Possibly* referencing the strange appearance of π but I doubt it. Anything can be significant if you believe hard enough, anyway.--162.158.158.60 20:30, 8 July 2024 (UTC)

How does adding a new branch to a railway line reduce congestion? Isn't this more like a highway? 141.101.105.47 23:30, 8 July 2024 (UTC)

Read about the 2nd avenue subway. 172.70.111.168 02:22, 9 July 2024 (UTC)

What is "thrembo"? Your favorite aura doggo (talk) 04:12, 9 July 2024 (UTC)

I think the whole section can be removed. The point is to explain the comic, not to describe what is seen (unless it's relevant for the explanation, which, so far, seems not be the case). "Various symbols" should cover it. Elektrizikekswerk (talk) 06:35, 9 July 2024 (UTC)

The symbols seem well chosen TBH, I can totally see how they substitute for 4, 5, 6, 7, 8 162.158.146.32 14:42, 9 July 2024 (UTC)

Except that, according to the title text, they should be 4, 8, 16, 32, 64. 172.71.242.159 15:59, 9 July 2024 (UTC)

I think that the express train travels on the regular number line, so I think the second branch parallels the regular number line. Thus, 4, 5, 6, 7, 8. Sarah the Pie(yes, the food) (talk) 02:11, 10 July 2024 (UTC)

Mathematicians been there, done that: https://en.wikipedia.org/wiki/Non-standard_model_of_arithmetic Although a nonstandard model of the integers can't branch by Peano axioms. 172.71.160.71 15:08, 9 July 2024 (UTC)

Hold my beer! [Prompts Claude 3.5 Sonnet to create a non-standard model of arithmetic.]

"Here is a non-standard model of arithmetic consistent with the Peano postulates:

Axioms:

∃0, ω : 0 ≠ ω

∀x : S(x) = x + 1 if x ∈ ℕ; S(ω) = ω

Theorems:

T1. ∀n ∈ ℕ : n < ω

T2. ∀n ∈ ℕ : n + ω = ω

T3. ω + ω = ω

Lemma:

L1. ∀n ∈ ℕ : S(n) ≠ ω

"Induction" Principle:

For any property P, if P(0) ∧ P(ω) ∧ (∀x : P(x) → P(S(x))), then ∀x : P(x)

Conclusions:

C1. This model "satisfies" Peano axioms while introducing a non-standard element.

C2. Arithmetic with ω leads to paradoxical results.

C3. Use of this model may violate conservation of sanity.

Oh, no! .... Tentacled one sleeps. Ph'nglui mglw'nafh Cthulhu. Accept this new soul. 172.70.210.103 03:24, 10 July 2024 (UTC)

Personally I would have branched off between 9 and 10, and had single character symbols for 10, 11, 12, 13, 14, and 15 so that you could do base 16 without having to use letters. Randell just lacks vision. Andyd273 (talk) 15:12, 9 July 2024 (UTC)

Letters are single character symbols! I think he should extend the number line with all the letters, getting to 36 (z) before needing any new symbolsPotatoGod (talk) 21:46, 9 July 2024 (UTC)