Discussion Forum Unit 2.docx - Discussion Forum Unit 2 Discuss how the limit allows a way to \u201cdivide by 0\u201d The question of division by 0 has never

Discussion Forum Unit 2.docx - Discussion Forum Unit 2...

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Discussion Forum Unit 2 Discuss how the limit allows a way to “divide by 0”. The question of division by 0 has never been a difficult one, although there might be issues to arise with it. It is said that the division by 0 is possible if the result is determined. To do so we need to expand the algebra. I think that serious doubts start to arise after studying rational numbers, when for any number x, except 0, is introduced the concept of the inverse 1/x and hyperbola graph: y(x) = 1/x graph It is obvious that when dividing 1 to very small number we get large numbers, and the less is x, the more becomes 1/x. So why can’t we say that 1/x=∞ is a certain number? The algebraic objection to this is as follows: Suppose that ∞=1/x is a number. Then all the rules that exist for ordinary numbers should apply to this number. In particular, on one side the relation 0* ∞ = 1 must be true, and on the other side, since 0 = 1 − 1, 0 * ∞ = 1 * ∞ − 1 * ∞ = 0. Thus, we get 1 = 0, and therefore follows that all numbers are equal to each other and are equal to zero. Indeed, since 1 * x = x is true for any number x, then 1 * x = 0 * x = 0. At this point, you probably ask yourself: “Well, isn't that complete nonsense?” Of course, this is complete nonsense, if we are talking about ordinary numbers. However, I emphasized the word “rules ” above for specific reasons.

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