Does Division By Zero Really Lead To Infinity?

I find it disturbing that even calculators make this mistake!

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Division by zero is a strange concept in mathematics. When you try it on a calculator (for example 4/0), you usually get an ‘error’ of some sort. Textbooks often come up with the term ‘undefined’. I originally tried to investigate this concept in the article: What Really Happens When You Divide By Zero?

After writing this article, I have received quite a few messages and comments from math enthusiasts. Some of these enthusiasts tried to provide alternative explanations, and some tried to prove that division by zero leads to infinity. In this article, I try to investigate the validity and merit of some of these approaches.

I see this is as more of a discussion amongst enthusiasts, and hope that we could all learn from it.

Negative Denominators Lead To Negative Results

In my original article, I tried to argue that multiplication can be considered as repeated addition. For example, (3 * 4) is the same as adding 3 to itself 4 times (3+3+3+3). Following this, I argued that division can be treated as the inverse of multiplication. For example, let us consider the following: 30 / 10 = 3 while 3 * 10 = 30. From these two equations, I could…