What does the $\Rightarrow$ arrow mean when showing working out in maths?

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How do we use it appropriately?

  • $\begingroup$ It means "then", "hence", "therefore", or any other words in the same spirit. $\endgroup$ – Tunococ Mar 14 '14 at 5:18
  • $\begingroup$ Typically this $\therefore$ means "therefore" and this $\implies$ means "implies". $\endgroup$ – Mr Pie Oct 23 '17 at 5:56

The $\Rightarrow$ notation means that if the function on the left hand side of the notation is true, then so is the function on the right hand side of the notation.

So consider $X\Rightarrow Y$. This means that if $X$ is true, then $Y$ is also true.

  • $\begingroup$ is it necessary/important to include? basically we could write that for any equation with ___ = ____ $\endgroup$ – confused Mar 14 '14 at 5:26
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    $\begingroup$ It is necessary to use this sometimes. For example: $$ x = 2 => x^2 = 4 $$ In this case we cannot say that they are equal. The => is more of an implication notation to show that logically both sides of the notation are equal. $\endgroup$ – lvella Mar 14 '14 at 5:30
  • $\begingroup$ Sometimes moving from one equation to the one below it is merely a matter of simplification of one or both sides. In these cases $\implies$ is not helpful (imho). But in other cases, the first equation is used to logically imply a different equation. And in those cases, it adds something by distinguishing the situation from the situation where you are merely simplifying. $\endgroup$ – alex.jordan Mar 14 '14 at 5:33
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    $\begingroup$ You can think of it as standing for the word "implies" if you wish. That is how I usually read it in my head. $\endgroup$ – ricardio Mar 14 '14 at 5:48
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    $\begingroup$ No, wouldn't that be $X \Leftrightarrow Y \ ?$ and this is where we get confused... $\endgroup$ – Mr Pie Oct 23 '17 at 5:56

It stands for "implies that". For example, $x = 2 \implies x^2 = 4$ - if $x$ is $2$, then it is obvious that $x$ squared is $4$; the symbol essentially shows a function here.


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