# Tagged Questions

**17**

votes

**3**answers

2k views

### What would remain of current mathematics without axiom of power set? [closed]

The power set of every infinite set is uncountable. An infinite set (as an element of the power set) cannot be defined by writing the infinite sequence of its elements but only by a finite formula. By ...

**0**

votes

**2**answers

534 views

### What constitutes the division between discrete and non-discrete math? Are there any math subject where it's being blurred? [closed]

I often heard about this division but always in a non-formal manner. What constitutes it? Is it a limit operation? Or a fundamental distinction between countable and uncountable sets? And what math ...

**7**

votes

**2**answers

891 views

### Are there uncountably many essentially inequivalent versions of Mathematics?

Hi everyone,
Disclaimer 1: logic and set theory are a long way from my field, so apologies in advance if I demonstrate extreme ignorance or stupidity, and please correct me if (when?) I write stupid ...

**13**

votes

**2**answers

823 views

### Is there a name for sets for which it is easier to test membership than to find members---and vice versa?

This is a question my son Bob asked me. For some sets it is relatively easy
to test for membership but a lot more difficult to find members, and for others
the reverse is true. Here is an elementary ...