/sci/ - Science & Math

Trump lost.

>>12617193
Trump lost what?
what does this have to do with my thread?

>>12617195
Trump lost and he is going to prison.

>>12617203
Is "Trump" some kind of mathematician?
was he working on this idea?
is that why he's going to prison?
am I in too deep?

>>12617186
You have to first construct 0, and 1 and the operations defined on them, the relation distinguishing 0 and 1 follows immediately. Use the peano axioms or something. "0" is some object in the set we call N, and "1" is succ(0), and we can prove these are different objects with different properties, and so on.
When all else fails, read Lang, try his basic mathematics book.

>>12617238
if this post isn't helpful, it's because I glossed over the OP, sorry

>>12617238
what is an objects, set, N, and succ()?

>>12617263
Peano's axioms are the basis for the version of number theory known as Peano arithmetic.

Peano's Axioms:

First rule: Zero is a number.

Second rule: If [math]a[/math] is a number, the successor of [math]a[/math] is a number.

Third rule: zero is not the successor of a number.

Fourth rule: Two numbers of which the successors are equal are themselves equal.\

Fifth rule: (induction axiom.) If a set [math]S[/math] of numbers contains zero and also the successor of every number in [math]S[/math], then every number is in [math]S[/math].

Now read this: https://www.docdroid.net/K1VENuF/basic-mathematics-serge-lang-pdf

>>12617281
>Zero is a number.
ok there is a number named zero.
but what's a number?
>second rule
what's a successor?
>zero is not the successor of a number
why not?
>Two numbers of which the successors are equal are themselves equal
what is equal? what is two?
> If a set
what's a set?
also how does this explain multiplication, divisions, exponentiation, etc.

>>12617291
>but what's a number?
It's a word called "number" and what it means is described in that post. You build them using zero and its successors.
>what's a successor?
the successor function or successor operation sends a natural number to the next one. The successor function is denoted by succ(n), where n is a placeholder for whatever number you shove into succ(). 1 is what succ(0) spits out.
>what is equal?
Equal is when two utterances share all the same properties, such that you cannot say anything about the first utterance that you cannot about the second utterance, because they are the same utterance in a math sense.
>what is two?
two "2" is a shorthand for succ(succ(0)).
>what's a set?
it's a linguistic device, like a word or phrase, and I attach properties to it as though they were things "in it", and I think about it like it was a box or a venn diagram. It's a symbol that I talk about and I associate things with that symbol and say they are members of the symbol or whatever. Fuck it.
>also how does this explain multiplication, divisions, exponentiation, etc.
Once you got the peano axioms, you build something called peano arithmetic, and it's explained in the link I sent you.

>>12617320
>You build them using zero and its successors
>the successor function or successor operation sends a natural number to the next one
>circular reasoning
kek what the fuck I wanted to talk about math you schizo.
what the fuck are you even on about?

>>12617326
troll gtfo