What number is after 99999999999999.99?

Answer 1

This question can not be answered due to the group of real numbers being infinitely large. To show what I mean, understand that 99999999999999.99 is not the entirety of the number, it can be expressed by separating the digits and adding each together to form the number, for example 999 can be rewritten as 9x102+9x101+9x100 and powers of higher values are ignored as they are preceded by 0 i.e. 999 can also be written as ...00000999.000... while this may seem obvious it is important to fully understand what this implies to understand you can never truly generate a number 'after' another one in the group of real numbers.

Now let's rewrite the original number, omitting the zeroes before it, so we get 99999999999999.99000000..... now one could argue that 99999999999999.99000001 is the next number by adding 1x10-8 on to the end, but then you could argue that 99999999999999.990000000000001 is the next number by moving the 1 down i.e. reducing the power so it's 1x10-15. It is because of this property of the real numbers that you can not generate a number that comes after it, for another person can just move the number further down the line and say it's smaller so therefore that is the next number.

In other words given a number x in the real numbers, the number that immediately follows differs by such a small amount that it is equal to x. A better way of saying it in proper maths language is, given a number x, and a sequence {xn} where each term gets closer to x, then the limit as n->infinity of |x-xn|=0