/sci/ - Science & Math » Thread #11941051

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Anonymous Sun 26 Jul 22:20:39 2020 No.11941051 View Reply Original Report

Quoted By: >>11941055 >>11941057 >>11941060 >>11941219 >>11941268 >>11941495

Are there proofs for simple arithmetic?
Like do we have a proof for 1+1=2?

Anonymous

Anonymous Sun 26 Jul 2020 22:23:08 No.11941055 Report

Quoted By:

>>11941051
it's pretty simple to prove from the peano axioms

Anonymous

Anonymous Sun 26 Jul 2020 22:23:12 No.11941056 Report

Quoted By:

we define 2 as the result of 1 + 1.

Anonymous

Anonymous Sun 26 Jul 2020 22:23:25 No.11941057 Report

Quoted By: >>11941059

>>11941051
most of the basic shit is definitionally true. no real proof needed

Anonymous

Anonymous Sun 26 Jul 2020 22:25:03 No.11941059 Report

Quoted By: >>11941070 >>11941071 >>11941231 >>11941239

>>11941057
Is there a proof for numbers actually existing?

Anonymous

Anonymous Sun 26 Jul 2020 22:25:51 No.11941060 Report

Quoted By: >>11941220

>>11941051
Karen a best Mosaic.

Anonymous

Anonymous Sun 26 Jul 2020 22:31:03 No.11941070 Report

Quoted By:

>>11941059
no. you need to start with some set of definitions/axioms
you might be more interested in metaphysics. I recommend starting with Descartes' Meditations and Spinoza's Ethics

Anonymous

Anonymous Sun 26 Jul 2020 22:31:23 No.11941071 Report

Quoted By:

>>11941059
that's axiomatic, can't really be proven (probably).

Anonymous

Anonymous Sun 26 Jul 2020 23:41:24 No.11941219 Report

Quoted By:

>>11941051
2 is defined as 1+1, but, yeah, there exist set-theoretic proofs of stuff like 2+1 = 1+2 or 2*3 = 6

Anonymous

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Anonymous Sun 26 Jul 2020 23:42:14 No.11941220 Report

Quoted By:

>>11941060
Amen.

Anonymous

Anonymous Sun 26 Jul 2020 23:42:36 No.11941223 Report

Quoted By:

yes here's all the proof you need.
.
.
..

Anonymous

Anonymous Sun 26 Jul 2020 23:45:12 No.11941231 Report

Quoted By:

>>11941059
Kind of?
You can prove that Presburger arithmetic is consistent.

Anonymous

Anonymous Sun 26 Jul 2020 23:47:11 No.11941239 Report

Quoted By:

>>11941059
They exist definitionally. You define them from axioms (set theory or type theory).

Anonymous

Anonymous Sun 26 Jul 2020 23:55:34 No.11941268 Report

Quoted By: >>11941310

>>11941051
>1+1=2
oddly enough there is
Bertrand Russel and Alfred North Whitehead spent 300 pages proving it with their Principia Mathematica in 1910
enjoy
https://en.wikipedia.org/wiki/Principia_Mathematica
https://archive.org/details/PrincipiaMathematicaVolumeI

Anonymous

Anonymous Mon 27 Jul 2020 00:18:27 No.11941310 Report

Quoted By:

>>11941268
Godel did later throw a spanner in the works.

Anonymous

Anonymous Mon 27 Jul 2020 01:25:28 No.11941495 Report

Quoted By:

>>11941051
ai priori axioms or whatever.

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