Originally posted by leisurelyslothFrom 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.
looks like letters to me 😉
EDIT: Cute whale miss (is it miss?) Nordlys.
Whalechicken's Faith Whale is cuter than mine, but I am still glad he shared this one with me.
Originally posted by Nordlysnumeral n: a word or symbol representing a number -- Merriam-Webster Dictionary
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.
In either case, I stand corrected. 😳
Originally posted by TheMaster37We'll have none of that. We're using the Peano axioms in this thread.
Don't forget the minus signs, possibly indicating negative nubers.
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.
By rule 4 negative numbers are not numbers.
Originally posted by XanthosNZAh, but the standard definition of the real number includes the axioms:
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]
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.
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Originally posted by XanthosNZPeanos 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.
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]
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."