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I'm trying to show that any two paths in a path connected space,are homotopic ( homotopic not path homotopic) ,any help?

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Hint. $[0,1]$ is contractible. So any path is homotopic to a constant one. Can you elaborate from here ?

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    $\begingroup$ So any path is homotopic to a constant one , so any two paths are homotopic to two different constant paths , since we're in a path connected space , I can find a path between these two constant paths and we are done , is this true ? $\endgroup$ – Butterfly Feb 13 '15 at 6:57

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