definite vs. indefinite

underworld

i have a small (i think) question:

a value of zero is a definite value, right? it's easily quantifiable. you either have it or you don't. and a value of 1 is also definite.

however, a value of infinity is not definite. it's an indefinite value.

now, the question is.... do quantifiable values become less definite the higher they go? in other words is 100 less definite than 1 or 0? probably not enough to matter. but what about 10E10 or 10E50 or higher values?

is there simply a line that is crossed where an infinite value becomes less definite? does the same apply to negative quantities? for example, is a quantity of -100 apples equally indefinite as a quantity of infinite apples?

d_leet

What do you mean by definte and indefinite, this seems much more a philosophical than mathematical quality.

underworld

well. a definite quantity would be "countable". for example, i can easily count whether i have zero apples or 1 apple or 20 apples. i would consider those values "definite".

i cannot easily count -4 apples or infinite apples. those values are not "definite". since there is no such thing as a -1 apple, then there is little difference between -1 apples and -100 apples. the same is true of infinite apples. there is little difference between infinite apples and infinite apples + 1 apple. therefore, those values are indefinite.

so the question is - is there simply a conceptual difference here? or is there a quantifiable gradient that occurs between 1 apple and infinite apples. in other words, is 10 billion apples somehow less definite than 1 apple? or is it just as definite all the way up to "infinity"?

d_leet

I still say that this is not really a mathematical quality or thing at all, but my opinion would be that any finite number is just as "definite" as any other. There really is no conceptual difference because the concept is not mathematical unless you conside definite and indefinite to be finte and infinite respectively as something can only be one or the other, and infinity is not considered a number so I guess you can vaguely say that it is thusly indefinite.

Office_Shredder

I think by definite you mean a natural number

Hurkyl

The extended real numbers [itex]+\infty[/itex] and [itex]-\infty[/itex] are definite things.
Projective infinity is a definite thing.
Each infinite ordinal number is a definite thing.
Each infinite cardinal number is a definite thing.
Each infinite hyperreal is a definite thing.

But a vague, nebulous concept of infinity is an indefinite thing.

HallsofIvy

All numbers are "definite". "Infinity" is not a real number but there exist various systems, such as the extended real numbers, in which they various infinities become "definite". It is the definition that makes it "definite".