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The reason 0 / 0 is undefined is that it is impossible to define it to be equal to any real number while obeying the familiar algebraic properties of the reals. It is perfectly reasonable to contemplate particular vales for 0 / 0 and obtain a contradiction.
10 gru 2018 · 0/n = 0 for all non-zero numbers n. You get into the tricky realms when you try to divide by zero itself. It's not true that a number divided by 0 is always undefined. It depends on the problem. I'm going to give you an example from calculus where the number 0/0 is defined.
Division by zero. The reciprocal function y = 1 x. As x approaches zero from the right, y tends to positive infinity. As x approaches zero from the left, y tends to negative infinity. In mathematics, division by zero, division where the divisor (denominator) is zero, is a unique and problematic special case.
10 sty 2018 · To put all of this into mathematical terms, dividing by 2 means finding a number (5) by which we can multiply 2 to get 10: 10 / 2 = 5 because. 10 = 2 * 5. If we could divide 10 by 0 (I'll call the answer X), we would be saying that: 10 / 0 = X because. 10 = 0 * X.
Proof 1. Let . Then we have (since ) (adding to both sides) (factoring out a 2 on the LHS) (dividing by ) Explanation. The trick in this argument is when we divide by . Since , , and dividing by zero is undefined. Proof 2. Explanation. The given series does not converge. Therefore, manipulations such as grouping terms before adding are invalid.
following proof. The proof also uses notation x1 to represent the multiplication of a real number x and the number 1. Proof: (Theorem 1) Let x be a particular real number. We want to prove that 0x = 0. We know from axiom 4 that: 1+0 = 1 Multiplying both sides by x gives: x(1+0) = x1 Using the distributive law gives: x1+x0 = x1
Therefore, it is not legitimate to divide both sides of the equation by , because that would be division by zero, which does not make any sense (as explained below). In essence, this proof boils down to saying "1 times 0 equals 2 times 0, therefore 1 equals 2".
