How can I verify if something is a function?

[Anonymous No.11682201]

I mean, something is a function if every preimage has only one image.

But I how can I verify this? Isn't it be possible that something that seems like a function, isn't a function?

[Anonymous No.11682226]

>>11682201
Intro to Proofs should include this.
The thesis is that for each X in domain there exists one unuque Y in range that f(x) =y, i. E. That there is some y equal to f(x) and that if there is z such that f(x) = z, then that z is y.
Prob not the anwser you wanted but the rest is situation deoendent.

[Anonymous No.11682305]

>>11682201
Some functions, like polynomials from highschool, are clearly functions, and I imagine the proof comes from some sort of math that shows there is no possible mechanism to get two values from the same point. Im not a mathemetician though I couldnt tell you how to show it i can just vaguely envision it.
For polynomials, it is probably that multiplication and addition of real numbers can only lead to one possible real number, so no real number will cause them not to be functions.

[Anonymous No.11682332]

>>11682201
>>But I how can I verify this?
veryfing this is called proving that a function that you have been given in math class is indeed a function

this is literally the first thing to prove in an exercise.

[Anonymous No.11682421]

>>11682201
I assume that OP lives in the set theory wonderland, where the notion of function is assimilated to the one of a functional graph. Apart from the fact that this is retarded, in this setting given f ⊆ P(A × B), to show it is a function you just have to show that for all x ∈ A, there exists a unique y ∈ B s.t. (x, y) ∈ f.

[Anonymous No.11682504]

>>11682201
f(2) = B
except on tuesday
then f(2) =C
so really your function takes two arguments, and is more like
f(w,x) -> Y
where w is the day of the week
then f is a function

[Anonymous No.11682623]

>>11682201
vertical line test

[Anonymous No.11682639]

fucking mathematicians

[Anonymous No.11682750]

>>11682201
a function f: X Y is just a binary relation R over X and Y which is just a set R ⊆ X × Y, you just need to prove

∀(x_m, y_m)∈R. ∀(x_n, y_n)∈R. y_n = y_m x_n = x_m

[Anonymous No.11682764]

>>11682750
moot ate my arrow signs

[Anonymous No.11682801]

>>11682201
currently having a girl rim my asshole

[Anonymous No.11682823]

>>11682201
It depends on how you define "function." and what information about that object you're given.
If a "function" is an incremental procedure given by parts that are provably functional (such as "map any number x to x+1"), then it can be proven by induction.
If you're given a non-finite relation, you may not have enough information to prove the relation is actually a (functional) graph.
But if you're just dealing with fucking textbook math, then all might-be functions are generally already given as functions.