1=0

prove me wrong.

NO U

1 != 0

qed

   1. 1 is a natural number.
   2. Every natural number is equal to itself (equality is reflexive).
   3. For all natural numbers a and b, a = b if and only if b = a (equality is symmetric).
   4. For all natural numbers a, b, and c, if a = b and b = c then a = c (equality is transitive).
   5. If a = b and b is a natural number then a is a natural number.
   6. If a is a natural number then Sa is a natural number.
   7. If a and b are natural numbers then a = b if and only if Sa = Sb.
   8. If a is a natural number then Sa is not equal to 1.
   9. For every set K, if 1 is in K and for every natural number x in K, Sx is also in K, then every natural number is in K. (It makes no difference here whether all elements of K are natural numbers.)

>>4
Prove axioms 1 to 9 are correct.

>>5
Look up 'axiom' in a dictionary.

>>5 You made me lol.

>>4
What is Sa, Sb etc?

>>8
Successors

ITT the peano axioms copy-pasted from wikipedia and a guy who doesn't understand logic or math arguing with them.

>>10
Please enlighten us then.

>>6
needs to grow a sense of humour

>>9
Ok but I don't see how >>4 proves that 0 is not 1.

>>11
he already gave the axioms.  i mean, i guess you could say 0 = 1 if you really want, but then you'll need another symbol to represent the additive identity, as you'll be using a different definition of 0 than the one thats usually implied.  (or a different definition of 1, depending on how you want to look at it)  as far as youre concerned, we just consider them different quantities for the sake of making them useful.

>>13
>>4 isn't proving anything.

If you use the Peano axioms (starting at 0 for convenience, otherwise you would need a bijection etc blahblahblah), you can just use the axiom that if a is a natural number, then S(a) is not 0. Since S(0) = 1, you can conclude that 0 is not equal to 1.

If you use the set theoretic construction you can say 0 is not 1 since {{}} is a proper subset of {{}, {{}}}, so the two can't be equivalent.

Or you can give your own construction of any number system you wish, but that's no guarantee it'll behave how you want.

>>3
GREAT WIN!

>>1
Is that 1 equals zero, or 1 is assigned to zero?

I feel the need, the need for weed!

Marijuana MUST be legalized.