
Home / TIL all numbers do not equal all other numbers
Today I learned through math that Aristotle was correct on the law of identify (i.e., A = A), and that everything that exists does have a specific nature. Specifically, all numbers do not equal all other numbers, and there are mathematical mistakes that lead to mathematical "proofs" that are (obviously) false. Can you find the error?
Consider that x = 1 and y = 1. Therefore, we can properly say that x = y.
If x = y, then it must be true that multiplying both sides of the equation by x is also true. In other words, x * x = x * y or, more simply, x² = xy.
Continuing, when you subtract y² from both sides of the equation, the equation is still correct. In other words, x²  y² = xy  y².
Another way to write the equation x²  y² = xy  y² is through factoring: (x  y)(x + y) = y(x  y).
To simplify the factored equation (x  y)(x + y) = y(x  y), you can cross out/cancel the (x  y) on both sides of the equation, leaving you with (x + y) = y.
As x = 1 and y = 1, when you substitute the values into the equation (x + y) = y, you are left with the conclusion that (1 + 1) = 1 or, more simply, 2 = 1.
Relativists of the world unite! There are no absolutes!
Or... you can find which premise is wrong that yields the apparent contradiction here. Ergo, even if relativism still rules in people's minds, absolutism still rules nature.
What did you learn recently?
DISCUSS!
Original posting by Braincrave Second Life staff on Mar 1, 2011 at http://www.braincrave.com/viewblog.php?id=488
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