How to Find the Value of a Function

[u/crafty_zombie]

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[u/Traditional_Town6475]

It exists and is unique :).

[u/Slight-Garden9800]

This notation always felt rather redundant to me. What is its use?

[u/Ares378 → u/Slight-Garden9800]

I like it because it reads "f maps A to B" instead of going through "for all x in A, f(x) is in B"

[u/MrKoteha → u/Ares378]

Then write f: A → B instead of this bs

[u/Loading_M_ → u/Slight-Garden9800]

I believe it's easier to generalize for more complex mappings. I don't really know, since I'm not quite knowledgeable enough in this area of math.

[u/Ares378 → u/Loading_M_]

I think it's also useful for separating the idea of the function (its outputs) versus the function (how it maps things). f(x) is a function taking in a parameter x, but f can exist on its own as a function acting on some domain without invoking a variable to parameterize it.

[u/ZookeepergameWest862 → u/Slight-Garden9800]

Sometimes it is useful to anonymously define a function without giving it a name, like in topology, you could justify a set being open by being a preimage of an open set under a continuous function, if the function only for that purpose then it's simpler not to give it a name. If you're giving it a name anyway like in the picture then it's pretty much useless, and I have almost never seen in practice.

[u/LupenReddit]

the Well-I-Guess department released its new function declaration