What is a finite number?

Question

zenmo · Answer

Question as posted, I would like some examples :)

mathstudent55 · Answer

A number that may be very large or very small but is not infinite.

zzr0ck3r · Answer

"A finite number" does not really make sense because then every number would be finite as $\infty$ (all types of infinity) is not a number.  "A finite number of things" makes sense. That would be any set of things where the cardinality of the set is finite. In other words there is some whole number of things.

skullpatrol · Answer

Any integer is an example of a finite number: $$\Huge ..., -4, -3, -2, -1, 0, 1, 2, 3, 4,...$$

zzr0ck3r · Answer

then it makes no sense to call it a finite number.... I have never heard "finite number" used this way. And negative finite really makes no sense.

zzr0ck3r · Answer

first thing you get when you google https://www.mathsisfun.com/definitions/finite-number.html

skullpatrol · Answer

"A definite number. Not infinite. In other words it could be measured, or given a value."

Negative temperature is just as measurable as positive temperature.

zzr0ck3r · Answer

what is the measure of a number?

skullpatrol · Answer

Numbers measure quantities. 
 
For example, the absolute value of a number may also be thought of as

the distance between the graph of the number and the origin on a number line.

zzr0ck3r · Answer

lol ok, again by your definition, every number is finite.

mathstudent55 · Answer

A system of 2 linear equations whose lines intersect has exactly 1 solution. The number of solutions is finite.
If the two equations graph as parallel lines, then the system has zero solutions, again, a finite number of solutions.
If the two equations are two different forms of the same equation, then their graphs are the same line. In this case, every point on the line is a solution of the system of equations. The number of solutions is infinite since it cannot be counted.

zzr0ck3r · Answer

i.e. it is the amount of stuff in a set $A$ when $|A|<\infty$.

skullpatrol · Answer

"Infinity" isn't a number :-)

mathstudent55 · Answer

The set of whole numbers has an infinite number of elements.
The set of whole numbers less than or equal to 10 has a finite number of elements.

zzr0ck3r · Answer

Right but in set theory we say $|A|<\infty$  which means a set has finite cardinality.

And actually you should have said infinity is not a real number, it is a number in the extended reals.