Life is an amazing thing! Sometimes it gives us a surprise in the form of a kind of paradox over which you can break the brain in an attempt to figure out where the correct answer lies. The word "paradox" itself means a situation that may well exist in real life, but which at the same time cannot be logically explained. In addition, there is such a thing as “aporia”. This term refers to a fictitious situation, but quite understandable with the help of logical arguments.
Paradoxes are different: economic, legal, philosophical, chemical, physical, psychophysiological, logical, related to choice, statistical and mathematical. Apparently, they are not so few. Let's talk about how paradoxes in mathematics can sometimes be puzzling. By the way, they are good exercises for brain training. After all, he, like the body, also needs to be trained. For example, try to solve the following comic mathematical paradox.
Once upon a time there lived a master who had a pair of excellent but small-sized boots lying around in the attic. He decided to get rid of them and instructed his servant to sell them at the market for 25 rubles. He went to carry out the assignment. At the bazaar, the servant saw a disabled person who had no left leg, and the right one was wrapped in some rags. It was autumn in the yard, the servant felt sorry for this man, and when he asked him to sell his right boot at half price, he agreed, although he understood that hardly anyone would need the rest. So, he received 12.5 rubles. The servant was about to return to the owner when the second one-legged disabled person turned up in his eyes, already without his right leg, who also needed shoes. He sold the remaining left boot for 12.5 rubles and was pleased to return to the master. The owner, after hearing this story, began to reproach the servant for not making an unhappy discount. He gave him 5 rubles and instructed to find those two buyers and divide the money between them. The servant, too, wasn’t bastard and decided that something should be laid for him too. Therefore, he took 3 rubles to himself, and each disabled person gave one ruble. Now, if you count together the money that the servant took for himself, and the money that people with disabilities ultimately paid, you get 3 + 12.5-1 + 12.5-1 = 26 rubles. But boots, after all, at first cost 25 rubles. Hence the question: where did the extra ruble come from? The answer to this mathematical paradox will be given a little later, so as not to deprive you of your own pleasure to figure out how it happened. In the meantime, we note that in addition to the comic, there are also serious paradoxes that are tormented by more than one generation of scientists and which sometimes cause heated debate.
Take, for example, the paradox of time, which is also known as the paradox of twins. In 1905, none other than Albert Einstein formulated a theorem that spoke of relativists time dilation. Its essence is that if at the same point two identical watches are located, showing the same time, and then some of them move along a closed curve at a constant speed until they again appear in their original place, then as a result they will show a different time compared to a clock that was motionless. Oddly enough, but the numerous experiments that were conducted with a macroscopic clock and elementary particles suggest that this is quite possible and the theory of relativity works in this case too.
Well, it's time to explain our mathematical paradox with boots. The extra ruble appeared because three rubles of a servant were added to the amount of money paid by people with disabilities (23 rubles), and this is not true. Servant money should not be added, but taken away. At first, the boots cost 25 rubles, but after the discount they began to cost 20. So everything fits together. If you have managed to independently solve this comic mathematical paradox, I congratulate you! And if not? Then try to solve other paradoxes in mathematics. In any case, this will increase the acuteness of your thinking. And who will refuse such a thing?