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Here’s a classic puzzle: you are a rather evil King. You have 1000 bottles of wine. Exactly one is poisoned. You need to find out which one. You have 10 prisoners. You can use them to test the wine. Now, … Continue reading
I was very excited to learn that there is a song titled Smooth Operator. Unfortunately, its actual content turned out to be very disappointing. Pity. We need more songs about smooth operators. And dense sets, and Banach spaces.
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