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I was given a definition.

A symmetry of a plane figure $F$ is an isometry that maps $F$ to itself, that is, an isometry $f:R^2 \to R^2$ such that $f(F)=F$.

I don't really understand this because is $F$ not a collection of points and the domain of the function consists of single points in $R^2$?

Can someone help me out? Thanks.

Rócherz
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hitherematey
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1 Answers1

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Yes $F$ is a subset of $R^2$.

$f(F)$ is shorthand for the set $\{f(x) : x \in F\}$. The statement "$f(F) = F$" is a set equality.

angryavian
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  • Is that something you cn do with functions? if you are not considering just a single point you can input a set of points and it will give the image set of all them point? – hitherematey Nov 23 '18 at 03:27
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    Yes. Sometimes we want to look at the range of a set $S$ and denote this set as $f(S).$ – Sean Roberson Nov 23 '18 at 03:47