Meggidon... let me give you a simple example. Take the function 1/x (that's "one divided by x"). Plug in 100 for "x". Then 1,000. Then 1,000,000. Keep plugging in bigger and bigger numbers. What do you get? Smaller and smaller numbers, closer and closer to zero.
Now, let's reason on that a little. Will the function ever actually equal zero? No. One doesn't divide into zero. You can't multiply zero by anything and get one.
How about a negative number... will the function ever be negative? Again no, because a positive number divided by a positive number is always a positive number. That's one of the basic rules of division.
So as long as you keep increasing the value of x, the function will keep getting closer and closer to zero, but will never actually reach it. Thus we can say that the limit of 1/x approaching infinity is zero.
Mathematicians have more formal techniques for determining limits, but that's the basic concept.
Onacruse
And yet we have a discrete symbol for it!...
Of course! We also have a discrete symbol for God. Anything we can conceptualize, we can symbolize; that's what thinking is, the manipulation of symbols.
we really understand what it means
We do understand what it means. It means "without end". The concept of "without end", however, is very obviously not a number.
If the 'hour' leg of this clock is moved an infinitesimally small angle away from verticle, how long will it take that leg to move down to 6 o'clock?
Ah, but that's a false paradox. If infinity is not a number, than infinitesimal is also not a number. That's precisely why mathematicians use limits.
An alternate solution to the paradox would be to refer to the discontinuity of space, but I prefer mathematical answers to physical ones.