Flashcards
2021-10-28
If you are told “$m$ is the smallest natural number such that $\frac{1}{m} \le q$”, how could you formalise this mathematically??
$$ \frac{1}{m-1} > q $$
What trick comes up a lot in dealing with inequalities??
Coming up with two separate inequalities with a shared term and sticking them together.
What’s a trick for approximating something like $\frac{3}{13}$??
Taking the reciprocal and considering what numbers it is sandwiched between.
If $$4 < \frac{13}{3} < 5$$ what is $$\frac{3}{13}$$ between??
$$ \frac{1}{5} < \frac{3}{13} < \frac{1}{4} $$
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date: 2021-10-28 13:56
summary: can you write all numbers between 0 and 1 as sums of distinct integer reciprocals?
tags:
- '@?public'
- '@?mat'
- '@?notes'
- '@?maths'
title: MAT - Paper 2018 - Q6