metric

introduction

%%visits: 4 The metric is a abstraction of a distant function using only sets. ## intuition Positivity:~ needs to be 0 if and only if equal arguments of the function. Needs to be positive. Symmetry:~ d(x, y) = d(y, x) Shortest distance :~ [[triangle_inequality]]

We can say two metric_space s are equivalent if any sequences tend to the same number. ## rigour {{file:../figures/screenshot_20220210_121315.png}} %% ==exam clinic ## examples and non-examples The Euclidean metric, which will be referred to as the usual metric. The discrete metric, which is one of the best tests for intuition.

%% ==resources tags math__metric_spaces_and_topologies:

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