Symfony Profiler

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            "content": "<p>Functions on real numbers are incredibly werid.<\/p>\n<p>There are continuous but nowhere differentiable functions.<\/p>\n<p>There are continuous and monotonically increasing function that goes from 0 to 1 (i.e. surjective function [0,1] \u2192[0,1]), where it \u201calmost never\u201d increases; specifically, if you pick a point at random, you will get a 0 derivative on that point with probablity exactly 1 (not <em>almost<\/em> 1, but <em>exactly<\/em> 1, no approximation here).<\/p>\n<p>More impressively, you can have function that is continuous, but you cannot find a connected path on it (i.e. not path connected). In plain word, if anyone told you \u201ca function is continuous when you can draw it without lifting your pen\u201d. They have lied to you.<\/p>\n",
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                "content": "Functions on real numbers are incredibly werid.\n\nThere are continuous but nowhere differentiable functions.\n\nThere are continuous and monotonically increasing function that goes from 0 to 1 (i.e. surjective function [0,1] \u2192[0,1]), where it \"almost never\" increases; specifically, if you pick a point at random, you will get a 0 derivative on that point with probablity exactly 1 (not *almost* 1, but *exactly* 1, no approximation here).\n\nMore impressively, you can have function that is continuous, but you cannot find a connected path on it (i.e. not path connected). In plain word, if anyone told you \"a function is continuous when you can draw it without lifting your pen\". They have lied to you.\n\n",
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