What is the difference between "divide" (÷) and "upon" (/), if any what is the role they play in maths and physics? I want to know why we perform this operation in mathematics.
Why do we need to divide?
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0thank you Andres for answering it could be the possible one – 2017-02-25
1 Answers
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There are many equivalent definitions for the operation, but it is usually not "division" that we are concerned with, but instead the operation $x \mapsto y$, where $x \cdot y=y \cdot x=1$, in other words, $x \mapsto x^{-1}$ where the latter is multiplicative identity. Naively, it helps us to solve problems like:
$$xy=xz.$$
If there existed a multiplicative inverse $x^{-1}$, then we could of course conclude that $y=z$. Without that, we are kind of in a bind.
Usually, $y \cdot x^{-1}$, is what I would call "division" whereas it is usually denoted $\frac{y}{x}$, which is essentially the same, but looks a little different.
Given a reasonable structure (say a ring with unity) we can algebraically construct the "field of fractions" which heuristically gives $x$ a multiplicative inverse if it does not already have one. People do this all the time to construct $\mathbb Q$ etc.
This just goes to show that we really want these things to exist-- it makes algebra many times simpler when we have such an operation.