can all of mathematics be derived from 1+1=2?
>>7983421
Using only that 1+1=2, what's 3+4?
>>7983421
In the everyday sense of "1+1=2," no, it cannot. For example, you cannot say that there exists an empty set from the above statement.
If you want to consider "1+1=2" in a more rigorous sense, then learn how to bait better and actually try to define it.
>>7983428
1+1=2
2+1=3
3+1=4
1+1+1+1+1+1=7
how can we prove 1+1=2?
>>7983455
It's axiomatic?
>>7983455
property of real numbers
What do you mean by "derived from"?
Anyway, no
>>7983421
All math was derived ultimately from counting on 10 fingers.
Theoretically, you should be able to prove stokes theorem using only your 10 fingers.
>>7983469
1+1= more than 2 if we apply some biology, If you know what I mean
>>7983455
The standard axioms of Natural numbers give a 0 and function s that is injective and such that 0 is not in its image (you can think of it as the "successor" function), with some other axioms including the scheme of recursion
The sum is defined recursively: for every x, y
x+0 = x
x+s(y)=s(x+y)
1 = s(0) by definition
2 = s(s(0)) by definition
1+1=2 comes from the above definitions
>>7983463
no it wasn't
first time on /sci/, is every post a bait in here?
>>728486
Peano axioms
>>7983421
no you dip
>>7983455
they're sets which really exist in the world, like everything except the set of all sets which don't contain themselves - which is the only known set to not exist.
>>7983421
It can be derived from -1 + -1 = -2
>>7983421
simplest arithmetic would be base 1
1+1=11
1+1+1=111
1+1+1+1=1111
11+111=11111
in base 1 the numbers grow large very fast, so you can use more symbols (higher base) to compress the numbers a bit
1+2+3=6
9+9=18
now if you want to add multiple times and writing it down takes too long, like;
10+10+10+10+10=50
you can use a symbol for repeated addition: *
5*10=50
and so on
someone wants to do anti-multiplication and division is born
subtraction, negative numbers, fractions, etc
eventually you get all of today's math and beyond
Can numbers asexually reproduce?
>>7983566
why don't we use base 1000000000000000000000000 for ultimate compression?
>>7983421
All of mathematics can be derived from being able to tell one object apart from another.
>>7983455
Proof by contradiction.
No. However, all of mathematics, including 1+1=2 can be derived from the fundamental theorem of barnett arithmetic, namely that the sum of the natural numbers is exactly -1/12.
>>7983454
>2+1=3
>3+1=4
>1+1+1+1+1+1=7
None of this comes directly from the fact that 1+1=2
>>7983845
Too many symbols to memorize
>>7983455
Better start reading.
>>7983428
1 + 1 = 2
Therefore,
(1 + 1) + 1 = 2 + 1
1 + 1 + 1 = 3
And also,
(1 + 1 + 1) + 1 = 3 + 1
1 + 1 + 1 + 1 = 4
So,
3 + 4 = (1 + 1 + 1) + (1 + 1 + 1 + 1)
But to answer OP's question: its fucking basic arithmetic. Of course in some sense, "all of math" is derived from it, in the sense that its a basic foundation for real math.
>>7985904
>(1 + 1) + 1 = 2 + 1
>1 + 1 + 1 = 3
Whoa there buddy, who said you get to assume + is associative?
>>7984746
>untyped set wankery
>>7983428
3 and 4 are definitions so you need those
