Number Theory Vs. Real Analysis
Here's the dirt on how these objects relate to one another:
The machinery of real analysis can often be used to prove certain facts in number theory. For example, if you want to demonstrate that a certain number theoretic function is increasing, if it has an obvious extension to the whole real line, you can try showing the extension has a positive derivative.
In turn, the real analyst can make herself more cultured by studying certain generalizations of the reals which generally fall in the realm of number theory: for example, the completions of the p-adic numbers.
In turn, the real analyst can make herself more cultured by studying certain generalizations of the reals which generally fall in the realm of number theory: for example, the completions of the p-adic numbers.