function math

introduction

This is some sort of mapping, used to add rigour to math, such as addition, subtraction. Among many other things that I hope to document in the future.

intuition

A map, from the domain to the range.

rigour

injectiv := one-to-one := if f(x1) = f(x2) ⟹ x1 = x2. This intuitively means that each input maps to a unique output.

surjectiv := onto := If for f : A → B, ∀y ∈ B, ∃x ∈ A : y = f(x)f is a surjection. AKA Let f : X → Y. We say f is surjective if for all y ∈ Y, there exists x ∈ X such that y = f(x). This intuitively means that for every possible output there is some input that is sent to it.

bijective := invertible := injective and surjective.

natural domai := This is an informal term to describe a domain that is natural. That is to say for what domain is the function well defined, so no division by 0 or no logs of negatives or negative of sqrts

exam clinic

resources

[[set___11_06_2022__090230149]] TODO

tags math

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