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As you know, there exists a bijection . Cantor demonstrated that. You even know how to construct this bijection: if and their decimal expansions are and then . It may be slightly more complicated than that, because in order to … Continue reading
Yes, yes, you have already seen this highly awesome video and you are aware of Smale’s paradox. But for as long as there is a possibility, no matter how remote, that some poor soul out there doesn’t know about these … Continue reading
If is a function, let us call a restriction of to . Let’s analyze one nice and pretty surprising fact concerning restrictions. Fact: Suppose we have a function of two variables and it’s restriction to every straight line going through … Continue reading
This could be the scariest prank ever, if I had someone to play it on: Step 1. Trick the victim into graphing this slightly modified version of Tupper’s SelfReferential Formula: in the region, say , , where n= 381025769433284440392319964900539302335 336506037124716737876327885349255244053 … Continue reading
This is Tupper’s SelfReferential Formula: what makes it interesting is that the set of points , for which the inequality holds, in the rectangle , , you will get this: Turns out that the graph of the formula resembles the … Continue reading
This is a pretty silly waste of time and computational power, but I wanted to try doing this for a very long time: I finally got around to making some “fractal” landscapes. The idea is that you if you generate … Continue reading
Weird fact of the day: Suppose , then: What does it really mean? It means: if you take some positive numbers , raise each to the power of n, add them all together, take the nth root of the sum, … Continue reading