I'm working on a pedagogical presentation in which I start by saying that two apples are equivalent things but not the same things. Therefore, my first slide is made of two distinct apples with the equivalence symbol between the two. Which one is appropriate and mathematically right ? This presentation is part of a research grant application and will be presented to a jury of mathematicians, so a bad choice of the symbol on the first slide could be heavily blamed on me.
Should I use $\simeq$, $\equiv$, $\leftrightarrow$ or ~ ? Or something else?