What Does Equality Mean in Math?

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In physics, an equation is telling you that two differently defined quantities are numerically equal to each other. But i recently realize that this does not always hold. For example, the schortenger equation says, h equals e i. It doesn't mean that using an operator is the same thing as energy. So in short, what does equality mean in math? I think there's a few things going on that i need to clear up here.

Welcome to the June 2022 Ask Me Anything episode of Mindscape! We are inaugurating a slightly different publication schedule, in which these monthly AMA will take the place of one of the regular Monday episodes, rather than being in addition to all of them. A slight tweak that will hopefully make my obligations a little more manageable.

These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). I take the large number of questions asked by Patreons, whittle them down to a more manageable size — based primarily on whether I have anything interesting to say about them, not whether the questions themselves are good — and sometimes group them together if they are about a similar topic. Enjoy!

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