By Erik Seligman
Were you aware that usually 2+2 equals five? That wheels do not regularly must be around? so that you can mathematically turn out there's a hippopotamus on your basement? Or tips on how to spot 4-dimensional beings as they go through your kitchen? If no longer, then you definately have to learn Math Mutation Classics. this can be a number of Erik Seligman's web publication articles from Math Mutation at MathMutation.com. Erik has been growing podcasts and changing them in his weblog for a few years. now we have amassed what we think to be the main attention-grabbing between them, and feature edited and arranged them right into a e-book that's usually concept scary, not easy, and enjoyable. This e-book is set utilizing math in specified methods; of interpreting issues we notice in lifestyles and utilizing facts to achieve the unforeseen. there's really a large variety of issues the following and so all age degrees and skill degrees will benefit from the discussions. Erik's exact point of view places a mathematical spin on every little thing from politicians to hippos. alongside the best way, you'll benefit from the assorted standpoint and optimistically it's going to open you as much as a touch extra out-of-the-box mind set.
Read Online or Download Math Mutation Classics: Exploring Interesting, Fun and Weird Corners of Mathematics PDF
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Additional info for Math Mutation Classics: Exploring Interesting, Fun and Weird Corners of Mathematics
5. You can also find various tricky “proofs” that 2 + 2 = 5 circulating the web, where many lines of complex algebra are often used. These many lines usually misdirect you from one invalid step, where a term t is replaced with the square root of t2 (it should really be the absolute value of that quantity), or both sides are divided by a term that equals 0. Here is an example of one of the simpler ones: 4 – 4 = 10 – 10 : Start out with true statement (2 – 2) × (2 + 2) = 2 × 5 – 2 × 5 : Rewrite both sides in a complex form (2 – 2) × (2 + 2) = (2 – 2) × 5 : Regroup factors on the right-hand side ==> 2 + 2 = 5 : Divide both sides by (2 – 2) As you have probably noticed, the last step divided both sides by 0, which is not algebraically valid, and results in nonsense.
If his label is on the door, we have a contradiction, since we defined Q as the set of labels of guests who are NOT in rooms with their label on the door. If his label is not in Q, then this guest is in a room without his label on the door – which means he must be in Q, due to the way we defined it. Thus we have another contradiction. So, no guest can be in room Q, and room Q must be empty, contradicting our assumption, and thus, the power set is strictly larger than the original set. And since every set, including a power set itself, has a power set that is strictly larger, this proof shows that there is an infinite class of infinities.
I tried doing a few more numbers on my hands, and was pretty hopeless. Could you imagine doing a series of these on each hand and holding the position long enough to complete a business transaction? In any case, can we do better than 10000? I also found an intriguing indirect comment on a yoga site, talking about a system of holding up individual joints or tips of each finger. This means that each non-thumb finger can represent four possible values, and the thumb can represent three, for a total of 4 × 4 × 4 × 4 × 3, or 768, combinations on each hand.
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