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# Should zero be considered a number?

Question #51985. Asked by Buck540. (Oct 27 04 10:55 AM)

Stew54

I think it depends what you mean by "number". If you are just talking about the basic numbers used for counting things then possibly it isn't, because you never start counting a group of things from zero. For any other defintion of "number" for mathematical purposes though, zero has as many functions as any other and so it is.

[Oct 27 04 2:18 PM] Stew54 writes:

It is, for example, the number which when added to x leaves x unchanged, as 1 is the number which when multiplied by x leaves x unchanged.

 Oct 27 04, 11:24 AM
Legolaschic

Mathematically speaking zero is not a member of the set of counting/natural numbers but it is a member of the sets: whole numbers, integers, rational numbers, real numbers, and complex numbers.

 Oct 27 04, 1:47 PM
kaylofgorons

If zero isn't a number, what goes between 1 and -1? Another mathematic purpose for it is anything to the power of zero equals 1. I'm with Legolaschic, it's an integer and belongs with the rest of those sets. By the way, I've heard that the idea of zero is a sign of intellectual achievement of ancient cultures.

 Oct 27 04, 4:36 PM
peasypod

In my opinion zero is the symbol representing the absence of any magnitude. It is also the cardinality of an empty set. I suppose it could be called a number whose sum with any other number is that other number....

[Oct 27 04 10:15 PM] peasypod writes:

Another interesting tidbit....

In terms of arithemtic, zero is the identity of addition (any number a has the property a + 0 = a) in the same way that 1 is the identity of multiplication. Hence zero is a very necessary number.

 Oct 27 04, 5:19 PM
gmackematix

As for zero, it is a number that has some quirky properties but quite a few numbers do. It has as much right to its place on the number line as -17 or pi.

If you are going to say zero doesn't belong because adding it to a number doesn't change that number, then we could argue one isn't a number because it doesn't change things it multiplies. Zero and one are known as the identities of the functions of addition and multipliation respectively.

Basically, a number is a property we ascribe to sets of objects. With a set of sheep, say, we count them using what are known as the natural numbers. By saying there are 3 sheep we are using a symbol, 3 (called a numeral), to indicate that this set can be paired off one-to-one with any other set with the property we call 3 (such as corners of a triangle). Any set that can be matched off with another set in this way is said to have the same cardinality. Clearly by removing one object from from each of two sets with the same cardinality they will still have the same cardinality (in our sheep example it will drop from 3 to 2). If we keep removing an object from sets with the same cardnality we will end up with empty sets. These have the cardinality zero (represented by 0). This is why zero is often given a pride of place at the start of the counting or natural numbers.

If the set is something like pounds in debt or credit then we need to include negative numbers and we have the set of whole numbers or integers with zero in the middle. To describe yet more complcated sets such as points on a line we need another sort of number called a real number, but yes, zero is included in that set of numbers too.

 Oct 27 04, 7:18 PM

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