The bottom line is. There are numerous, equivalent ways of defining the real numbers and each have the advantages and disadvantages in understanding. Any good i

The bottom line is. There are numerous, equivalent ways of defining the real numbers and each have the advantages and disadvantages in understanding. Any good introduction to analysis class will do a definition several times and prove equivalence. Infinite decimals in particular bring up the equality problem. If you're willing to think of the real numbers as ONLY infinite decimals, you avoid this confusion. But it's silly to always write .999... instead of 1.