But what is f(1.0) = f(0.999...): 0 or 9?
I have a quick question about single/multi-valued functions.
Given the function where f(x) = the digit in the "tenths" position of x in its decimal representation. An example is means that . It is obvious that this function is single-valued. But I can't find an argument to prove that.
It may well be that I'm over-thinking this.
I can't seem to get my head away from the graph. I'm suspecting a graph is not the way the text wants me to prove multi-valued-ness. Either way, I guess I've got the idea well enough.
Decimal representation is unique, except for infiniteley repeating nines which take the next highest integer by convention, so that they are also unique.
A sloppy proof of uniqueness is if a has two decimal representations, a-a = 0 is a contradiction.