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Is there some rule as to when I should use $=$ and when I should use $\iff$? For me, it seems like they are used interchangeably. If so, what is "best practice"?

J.G.
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Tomas R
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    I think $\iff$ a relationship between two statements, while $=$ is used with two quantities. –  Jan 11 '23 at 09:15
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    No doubt, someone will make this as technical as they can, but I would think in terms of logical statements for symbol $\Leftrightarrow$ and some concrete objects/quantities for $=$. – AlvinL Jan 11 '23 at 09:16
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    For example, it holds that $2x=4$ $\Leftrightarrow$ $x=2$. – AlvinL Jan 11 '23 at 09:17
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    These symbols are not equivalent. $=$ denotes an equality of objects (in $x^2+7x+6=0$, $x$ is a real number such that $x^2+7x+6$ is the number zero), while $\Leftrightarrow$ means “the logical statements on the left and the right have the same truth value”. $x^2+7x+6$ is not a statement; $x^2+7x+6=0$ is a statement, and $x^2+7x+6=0 \Leftrightarrow x=-6 \text{ or } x=-1$ holds. – Aphelli Jan 11 '23 at 09:18
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    See first comment above: we have terms (i.e. names), like $1$ and $1+1$ and we have formulas (i.e. sentences). We have to use $=$ with terms: $2=1+1$ and "iff" (and other connectives: and, or, not) with formulas: $lnot (1=0)$. – Mauro ALLEGRANZA Jan 11 '23 at 09:22
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    Many answers in the comments! $\ddot\smile$ – YiFan Tey Jan 11 '23 at 09:26
  • Never had this many comments so fast :) Thanks all! – Tomas R Jan 11 '23 at 09:28

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