Is it better to use `\Rightarrow`

or `\implies`

to symbolize logical implications? Why?

Also, if I write `\not \Rightarrow`

, I get a symbol that means "does not imply." But if I type `\not \implies`

, it doesn't look right. How do I get the corresponding "does not imply" symbol?

## Best Answer

To answer your first question, you should use

`\implies`

, not`\Rightarrow`

.`\Rightarrow`

is far too small to give a readable result and is not spaced properly. Knuth specially defined`\iff`

to be used for equivalence and`\implies`

is the same but for implication (from the`amsmath`

package). An implication is not a relation like`>`

and, therefore, needs to be spaced according to how it is used. Two thick spaces (which are about an en-space) precede and follow an implication because it's more important than a relation. (Basic rule of math spacing: the more important an operator, the wider the space around it). Compare the readability of the following formulas:The first line uses

`\Rightarrow`

and is the least legible because the main part of the formula (the implication) is difficult to identify. The second line uses`\Longrightarrow`

and is better, but there's not enough space to set the arrow apart from the surrounding symbols (the two inequalities are spaced as much as the arrow). Finally, in the third line (which uses`\implies`

), the additional space highlights the arrow from the rest and so improves the readability of the formula.Concerning your second question, the simplest way to negate nearly any symbol whatever its length is to use

`\centernot`

from the centernot package:Of course, wrapping

`\centernot\implies`

inside a`\notimplies`

macro like Werner did is a good idea.