Is it available a logical -mathematical demostration of the existence of zero?

Question

Would you mind to post it?

Answer 1

Not really.

Some ancient cultures didn't use zero in their mathematics. Have you ever seen a Roman numeral for zero?

And, we still avoid using zero in some situations. Wouldn't it make more sense to call the ground floor of a building the 0th floor, rather than the 1st floor?

Some axioms for arithmetic require zero. But, the existence of zero is usually given as an axiom, so it needs no proof.

Answer 2

...-3,-2,-1,0,+1,+2,+3...
A ring R is said to satisfy the left (right) cancelation law if and only if R has no 0 divisor.

Proof: Let R satisfy the left cancelation law and suppose ab=a*0, whence by cancellation b=0. Thus a is not a left zero divisor.

Answer 3

Generally no.


0 is the "additive identity" which must be postulated along with all the other rules for real number arithmetic.

Is some other set of assumptions possible in which 0 is not assumed, but can be proved? Probably.

Answer 4

first proof is to subtract one from one ... you get zero... it is a defined number that exist

Second it is the additive identitiy. It is the number that if you add it to any other number you get the same number back...

if you add 1 to -2, you get -1... if you add 1 to -1 you do not get 1, so there exist something between 1 and -1... that thing is zero.

Answer 5

yes there is