The value of a whole number

[rafark]

So we know whole numbers can be broken into decimals. eg:0.1, 0.2, etc.

We have currencies which define a specific number of pieces a whole value can be divided into, for example, "1" can usually only be divided into 100 pieces: after "0.99" comes "1".

What happens when we don't define such amount? For example, in another context, after 0.99 comes 0.100, then 0.101 and so on. It seems we can keep increasing the count endlessly, eg: 0.1000, 0.10000, 0.10000000 ad infinitum.

So the cuestión is, what is the real value of a whole number? Are decimals infinite?

 

[MacDawg]

Yes

 

[cube]

A whole number is a real number.

 

[dukebound85]

Yes. What is the question?

 

[NoBoMac]

Technically, if I remember my math lessons, a whole number is an integer greater than zero. Some include zero in the set. But basically, anything that does not have a decimal point.

What you are asking about is significant digits and converting a whole number to a real number. Or in computer-ese, floating point numbers. And yes, the decimal point can go on infinitely (see: value of Pi).

https://en.m.wikipedia.org/wiki/Floating-point_arithmetic

 

[cube]

Floating point numbers can only represent some rational numbers exactly in a computer, even with an arbitrary precision library, because of finite storage.

If the universe is infinite, you could make an infinitely growing computer but would never end building A LOT of numbers (as many as ALL real numbers).

You can improve that by representing a rational number as a pair of arbitrary precision integers.

And then you have symbolic representation.