Implication of Statements "When" and "Just When" I'm not really sure if this is the right part of SE for this question or if it should be in the Meta part - if it should be, then let me know and I'll change it!
Anyway, here's my question:
What is the precise difference between the statements "When" and "Just When".
I think that I have the answer, but would value confirmation.
Statement 1: {We have A when B}. So we can have A but not B (ie, B $\nRightarrow$ A), but if we have A, then must have B (ie A $\Rightarrow$ B - this would be consistent with the usual contrapositive)?
Eg, let $a,b \in \Bbb N$: $a \ge b$ when $a \ge b + 2$, but not just when $a \ge b + 2$; but we can have $a = b$ which does not satisfy $a \ge b$.
Statement 2: {We have A just when B}. So now whenever we have A, we also have B (ie, A $\Rightarrow$ B), but if we have B, then we also have A (ie B $\Rightarrow$ A).
However, consider an adaptation of the the example above: $a \ge b$ just when $a \ge b - 1$; however, we do not necessarily have $a \ge b$ when $a \ge b - 1$. Is this (adaptation) correct?
Thanks! :)

Interpreting "A when B" as $A \Rightarrow B$ isn't really consistent with the english language. If I say "I get wet when it rains", that means (at least to me) that rain implies getting wet, not the other way around. I.e., whenever it rains I get wet, but I might get wet even if it doesn't rain (if I, say, jump into the pool). I'd thus read "A when B" as $B \Rightarrow A$.
For "A just when B", I agree - it means $A \Leftrightarrow B$. Just whenever A is the case, so is B, and conversely whenever B is the case, so is A.
