This is actually a pretty good habit to get into when doing math. Lots of plausible-sounding conjectures actually do turn out to be false because math can allow for some pretty strange-seeming things. For example, you can have functions that are continuous everywhere but differentiable nowhere, or uncountable sets with length zero, or all kinds of other crazy things.
This is actually a pretty good habit to get into when doing math. Lots of plausible-sounding conjectures actually do turn out to be false because math can allow for some pretty strange-seeming things. For example, you can have functions that are continuous everywhere but differentiable nowhere, or uncountable sets with length zero, or all kinds of other crazy things.