I am working through an Analysis textbook and came to the construction of the reals using Cauchy Sequences. I understood the proof more or less but far from completely / intuitively.
I have no image what exactly a sequence is.. does this construction mean we can have a special sequence to represent each real number we want? If so, how would a sequence for let's say $ \sqrt2 $ look like and what is the function creating this sequence?
I would be glad to get any information which could help clear this up. Of if you have any good intuition to share :)