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There are a lot of names in mathematics that are common names; limits, sequences, absolute, smooth, continuous, etc.. I daresay the named-after-people definitio
by jhanschoo 11y ago
There are a lot of names in mathematics that are common names; limits, sequences, absolute, smooth, continuous, etc.. I daresay the named-after-people definitions are in the minority.
You also have definitions named after common intuitions like openness and closeness in topology that end up confusing people because after some thought, mathematicians have found that some sets are open and closed at the same time, but that's not possible in most physical objects.
Ultimately, I think that the unfamiliar-name problem is just something that people have to get over with. We learn all the time the difference Coca-Cola and Pepsi, Apple and Google, and so many other unfamiliar names.
- yummyfajitas 11y agoClosed sets are actually well named - a closed set is a set which is closed under the operation of taking limits. It's open sets which are badly named. Open sets are used for distinguishing between points - i.e., two points (x,y) are topologically distinct if you can find two disjoint open sets x \in X, y \in Y with X \cap Y == \emptyset. Coming up with a collection of sets which are good for this purpose is totally NOT the opposite of being closed. "Distinguishing sets" might have been a better name.
- jandrese 11y agoYes, but when someone is writing down the equation they don't say: "Sum of this set from 1 to infinity" They use a capital Sigma, and scatter the symbols around it. The terms exist, but they're not present in the equations!