Prove that 1=1

no it isn't

Do you accept that, by the way we construct equality as an equivalence relation, it must be true that a=a for all valid a?

1=1.
/thread

quora.com/How-can-neural-networks-learn-to-solve-math-problems

It's not. Axioms are taken as true.
You can't prove an axiom. The axioms are there so that proofs can be made. If an axiom is provable, then it's either not an axiom or your system is inconsistent or incomplete, i.e. Godel. For example in chemistry if you take protons, electrons, and neutrons as your axioms, you can show how hydrogen, oxygen, and the other elements are derived from those particles. But you can't show how a proton is derived from protons, electrons, and neutrons. Why is this shit important? Because a computer is stupid. At some point it has to make comparison it must have a fundamental list of operation that carries out without breaking things smaller.
In terms of symbols there are dumb shit that do not follow that rule. For example infinity does not follow flexibility. You can say that infinity = infinity + 1.

>You can say that infinity = infinity + 1.
that's wrong though

By definition of the word infinity, it's not. Infinity encompasses every value including infinity +1

A = { 1, 2, ... }
B = { 0, 1, ... } (add an element)
(A -> B)(x) = x - 1
(A

f(x) = x+1
f(1) = 1+1 = 1+1 = f(1)
1=1

infinity plus 1 is one more than infinity.

Yes and no. It's retarded but there's a lot of proofs that rely on accepting this condition. Infinite hotel paradox. Calculus. Infinite summations. -1/12.

Infinity isn't a quantity, it's merely a concept.

Infinities are quantities, one of their defining characteristics is that you can take or give any finite amount and they will remain unchanged

If you find a consistent system where you include "infinity" as a term, i.e. if you leave the reals as in pic related, then you may be able to prove
infinity = infinity + 1

That's not in conflict with
infinity = infinity
so long as you can't prove
0 = 1
e.g. by subtracting -infinity. The later isn't allowed in those systems, for that reason.
Besides, even if, some forms of contradictions can be dealt with in some systems.
en.wikipedia.org/wiki/Paraconsistent_logic

Coming back to your
>axioms are statements that can't be proven

Well as I said above in (), they can be proven in the framework there, but that's really just a semantically distinction.
But consider the following theory I just made up:
It's the same as Peano arithmetic for the natural numbers, except my theory has one more axiom:
3+5 = 8

Now are you gonna argue I can't prove 3+5 = 8 in my theory? I surely can, because even the naively weaker theory of Peano arithmetic can prove it.
Obviously, this axiom is just redundant.

You said
>axioms are statements that can't be proven
but in reality, what's true is only the following tautology:
>non-redundant axioms are statements that can't be proven from the other axioms of your theory

The above statement, however, doesn't prevent me from proving an axiom from itself.
E.g. P=>Q is only false when P is false and Q is true. Thus A=>A is alsways true. If a formula A is true, then we have
A and A=>A
and we can thus derive A by Modus ponens.
If you want to go out of your way and define and prevent a proof chain from being valid if the last proven statement is also and axiom --- okay. Nothing was won this way, though.

= is reflexive, Q.E.D.

Now fuck off you subhuman monkeyposter.

You can have a complete system but it won't be consistent. I prefer the practicality of mathematics in computation. Like I said, computers are stupid.
Sure, you can have 3+5=8 as an "axiom" for a computer, to which a computer will spit out as true whenever it runs across without question. But like you said, it's redundant because you can reduce it to 1=1.
The point is that if you keep reducing things and reducing things without reaching a point where there's a definite stop to make comparisons you'll end up in an infinite loop and nothing can be calculated.

The negation of anything is nothing, if it is not nothing, than what was negated was nothing.

The negation of anything added to the negation of anything is nothing, if it is anything, than anything was nothing.

Anything added to the negation of any thing is Anything. If anything is nothing, than the negation of anything was anything.

Therefore 1=1

Take your pedophile cartoons to

...

Axioms and theorems are interchangeable, in general.

Wildbereger asserts that the notion of equality exists when each side of a = has an even pairing of I's. Ie IIII = IIII is considered "equal" which just means that they appear at the same time in the ordered sequence of numbers.

If they are unevenly paired ie II = IIII, this would be meaning later in the sequence.

1 = 1 because they share an identical space on the number line. Its really all that is needed.

>Now are you gonna argue I can't prove 3+5 = 8 in my theory?

I'd argue you would be proving a proposition, not an axiom. 3+5=8 is not axiomatic because it is not self-evident, it can only be derived after you construct several definitions and algebraic axioms.

Axioms and definitions can not be proven, they are accepted as true. If an axiom is falsifiable, it is not an axiom. Using other axioms to prove an axiom is redundant because the other axioms must have also accepted the first axiom as true without proof.

it goes without saying that our usuaal hindu arabic numerals represent collections of I's, 4 is IIII 1 is I etc

Yes bravo, you can go the Wildberger route and criticize the way we've chosen to use words and historically grown framrworks while not offering an implementable formal framework yourself.
I agree that making axioms just formua on the same level/type as any proposition and thus susceptible as a formal result of a proof chain doesn't help conceptually working out the notion of "axiom". But the harm it does is small, and proposing the opposite (and thus crashing the standard proof theoretic framework in this regard) just introduces complexity.

Furthermore, it is of note that wildbergers fundamental assumption is a blank page, although it is implied that there exists a way to modify that with writing. There is, however, no notion of erasure or deletion

This has interesting analogues in respect to his rejection of infinity as a set ie containable/countable.

I am not criticizing anything. I am explaining to you what an axiom is.

Define "Define"

1+1=2
2-1=1
Therefore 1=1

You can't.
But if it wasn't true everything you did would be completely pointless.
A = A is the idea of identity. Something is what it is. If that wasn't true it would be impossible to know anything at all. Evidently you do know certain things, therefore it is reasonable to assume that it is true.

hahah pretty sad that sci can't even prove that 1=1, I guess all that math that you base your worldview on is bogus after all.

The really sad thing is that you don't even exist

1 + 0 = 0 + 1
1 + 0 = 0 + 1 = 1 + 0 = 0 + 1
1 = 1

>1 + 0 = 0 + 1
[citation needed]

What is that one. an electron? Do I have to prove here than another electron is exactly like an another electron?

Axiom.1)
>to represent values, relations and concepts; symbols are used
Axiom.2)
>the symbol "=" indicates both collections of symbols on each side of it are the same in value
>this symbol can only be used if both collections of symbols on both sides are the same value

"1" is a symbol that represents a value. I'll create a valid collection of symbols "1=1" which is valid because there is the same symbol on both sides of the "=" which represents the same values

If that was true wouldn't it mean that the universe was a simulation?

Can't do it, not even if sober.

or does it exist within itself?

additive identity
a + 0 = 0 + a = a