Originally posted by leisurelysloth looks like letters to me 😉
EDIT: Cute whale miss (is it miss?) Nordlys.
From Wikipedia: "A number is an abstract entity that represents a count or measurement. A symbol for a number is called a numeral." A number written in letters is still a number.
Whalechicken's Faith Whale is cuter than mine, but I am still glad he shared this one with me.
Originally posted by Nordlys From Wikipedia: "A number is an abstract entity that represents a count or measurement. A symbol for a number is called a numeral." A number written in letters is still a number.
Whalechicken's Faith Whale is cuter than mine, but I am still glad he shared this one with me.
numeral n: a word or symbol representing a number -- Merriam-Webster Dictionary
Originally posted by TheMaster37 Don't forget the minus signs, possibly indicating negative nubers.
We'll have none of that. We're using the Peano axioms in this thread.
1. 0 is a number.
2. The succesor of any number is a number.
3. If a and b are numbers and they have the same succesor then a equals b.
4. 0 is not the succesor of any number.
5. If S is a set containing 0, and the succesor of any number n is included in S then S contains all the numbers.
Originally posted by XanthosNZ We'll have none of that. We're using the Peano axioms in this thread.
1. 0 is a number.
2. The succesor of any number is a number.
3. If a and b are numbers and they have the same succesor then a equals b.
4. 0 is not the succesor of any number.
5. If [b]S is a set containing 0, and the succesor of any number n ...[text shortened]... b]S[/b] then S contains all the numbers.
By rule 4 negative numbers are not numbers.[/b]
Ah, but the standard definition of the real number includes the axioms:
a. There is an additive identity (0)
b. Every number has an additive inverse
c. There is a multiplicative identity (1)
d. Every number (except 0) has a multiplicative inverse
e. 0 != 1
c. and b. imply the existence of -1 as a real number.
Originally posted by XanthosNZ We'll have none of that. We're using the Peano axioms in this thread.
1. 0 is a number.
2. The succesor of any number is a number.
3. If a and b are numbers and they have the same succesor then a equals b.
4. 0 is not the succesor of any number.
5. If [b]S is a set containing 0, and the succesor of any number n ...[text shortened]... b]S[/b] then S contains all the numbers.
By rule 4 negative numbers are not numbers.[/b]
Peanos axioms is about natural numbers, not only numbers. -1 is not a natural number by these asioms, for that you have to have an extention to the natural numbers - the integers.
But of course -1 is a number. (Of which kind?) An integer. (Not a natural number?) No, there is no negative natural numbers. Not by the Peanos axiom of the natural numbers, anyway. (Why?) Zero is the smallest natural number. (Why?) "0 is not the successor of any natural number."