Say I have the four following logical statements, all over the domain of all integers.
I feel like they're all asking practically similar things, but I'm getting on confused on what exactly for all means. I'm writing what I think each statement is asserting literally, please correct me if I'm wrong:
- All integers are greater than each other? (This is the one I'm struggling the most with)
- There is an integer b that is less than all other integers
- There is an integer a that is greater than all other integers
- There is an integer a that is greater than an integer b
So if this is the case, I'm assuming that all are false except for (4). But in the event that I have correctly understood all four of these statements, how would you express something like how for all known integers, there is another integer that is greater and/or lesser than it?