>>12145486>maybe not PDE? I dunnoNot sure if you could count it as such since it's not explicitly PDE and it's a bit circular, but the existence of the rationals make the reals separable. That in turn gives you a million results in analysis and topology that you end up using in PDEs one way or another. Also see below.
>>12146418Like
>>12146428 already pointed out there are many proofs that rely on proving a result for the rationals and then extending it to the reals. The existence of inner products on normed spaces where the parallelogram law holds is an example, and that in turn gets used in PDEs to prove some results on Sobolev spaces.
