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**nomadreid** Thanks, wonderboy1953, but I would say that you have missed the point of the post. I put in , and your answer was essentially "it's useful, so use it". Of course one uses it, but I see a problem similar to the one posed by the paradoxes at the beginning of the 20th century: then, too, the day-to-day mathematics was not affected by the crisis in Foundations; the mathematics used was justifiable, but whereas the usage was correct, the justification turned out to be wrong, so one had to look for the correct justification. To give a more basic example: if a school student gets the right answer with a faulty method, he doesn't get any points. ("What is the length of the hypotenuse of a right triangle with legs 13 and 84."...."85".... Good. How did you get it so fast?"...." Simple. I saw that in the 3-4-5 triangle, the 5-12-13 triangle, the 7-24-25 triangle, the 9-40-41 triangle, and the 11-60-61 triangle, the hypotenuse was one plus the longest leg. This is apparently also such a case." Zero marks.)