/math/ - Mathematics

To give an answer you need to define what is "13.333... exactly". If you define it as an infinite string to the right, an algorithm that calculates it (using the rules of addition and multiplication) will print it in infinite time. Mentioning the algorithm here is for intuition, in fact if you define operations on infinite strings that way, it will do so. The nerds can refer to the axiom of choice.

(In your post you used the word "approximate". Ask yourself the question -- "approximate what?")

>>214
13.333... is the real number approximated by the sequence 13.3, 13.33, 13.333, ..., or in more precise terms, its limit.

When people say 1/3 = .333... or anything like that, by defining the right side so that it would be true, it's bad notation. 1/3 can't be written as a decimal expansion because the division always results in a remainder. But you can have a number where there is always an extra 3 added to the expansion, so it would be an unending number of 3s, like .3 + .03 + .003 and so on. I would like to use an infinite series here to make it neater but it's unfortunately defined according to limits so I will avoid it here as limits are not part of the discussion, only true values. If you do have such an unending string of 3s in the decimal expansion, it will not be equal to 1/3. since the difference between it and 1/3 is always greater than 0, no matter how long the string stretches. There are quite a few numbers that can't be written using decimal expansions, 1/3 is just one of them.

Paul Erdös has constructed a proof that the Copeland-Erdős constant is relatively normal.

Can someone help me understand the proof?