A Question about Infinity

[Thinking Skins]

I decided to ask this question in a new thread since I continuously see the statement being made that infinity is a man made concept.

So can somebody please tell me what infinity is?

And if anybody is familiar with irrational numbers, can somebody tell me how many digits there are in the number pi?

Also can somebody please solve the equation f(x) = the limit, as x approaches 0, of 1/x?

[Thinking Skins]

We don't use infinity when there is no answer; we use it when it IS the answer. If you draw a circle, and you try to measure it in the real world using real rulers and real pieces of string, you will find that the ratio between the circumference and the diameter is an irrational number called pi.

Pi is the answer - it's not a guess, it's not an approximation, and we don't use it because a finite answer is not forthcoming. We use Pi because it is the answer - in fact, it is a finite answer. Also, Pi can only be represented by an infinitely long decimal, infinitely long series, or infinitely long fraction.

If you believe in circles, you have to believe in infinity. You can't have one without the other.

To further your argument, lets look at the set [0, 1] = { the set of all numbers between 0 and 1, including both numbers } .

How many elements are in this set?

The answer us UNCOUNTABLY INFINITE.

What about the set [0, 1] <FONT FACE="Symbol">Ç</FONT> Q = { the set of all numbers between 0 and 1 that can be written in the form a / b }.

How many elements are in this set?

The answer is COUNTABLY INFINITE.

Those are two different infinity's both of whose definitions MATHEMATICIANS CAN PROVE, and the FACT is that UNCOUNTABLY INFINITE is a larger set that COUNTABLY INFINITE.

Infinity is not an imaginary number. [sqrt](-1) is an imaginary number. Infinity is just as true as 0 or 1.