# Tag Info

## New answers tagged mathematical-analysis

2

In my opinion whether this proof is correct or not depends on the actual wording of the question. This recursive argument shows that the statement is true for 100 numbers (since it is true for 2, 3, 4, so we eventually reach 100) It also shows that the statement is true for 1000 numbers (we eventually reach 1000). For any fixed natural number this is a ...

0

I think there's a lot of variation in content of precalculus. I had a semester of theory of functions and semester of analytic geometry, both including some aspects of calculus itself, in a strong public school. But in some ways you could have skipped that stuff and moved right into calculus after algebra two trig. Rotations were definitely included. And ...

1

I'll give a less elegant answer: because the dilations and translations are easy to understand and implement. If we were interested in preserving shape under the transformations then surely rigid motions or orthogonal transformations would be a better scope for the discussion. Sadly, highschool students (in the USA) do not typically learn linear algebra, ...

2

We can think of these transformations from two perspectives: as mappings of the plane or as graphs of pre/post composition of the function. For instance, the map $T: \mathbb{R}^2 \to \mathbb{R}^2$ given by $(a,b) \mapsto (a+2,b)$ is the translation of the plane two units to the right. Let $\phi: \mathbb{R} \to \mathbb{R}$ be the function $\phi(x) = x-2$. ...

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