2 – Number Set Notations and Universal Quantifiers

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Number Set Notations & Universal Quantifiers

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Author Jonathan David | AuthorJonathanDavid.com

Number Set Notations

Real Number Set, $\mathbb{R}$
$\mathbb{R}=(-\infty,\infty)$ all real numbers
Complex Number Set, $\mathbb{C}$
$\mathbb{C}=\{a+ib|a,b\in\mathbb{R}, i=\sqrt{-1}\}$
All Integers, $\mathbb{Z}$
$\mathbb{Z}=\{\dots -3,-2,-1,0,1,2,3,\dots\}$
Positive Integers (natural numbers), $\mathbb{N}\equiv \mathbb{Z}^{+}$
$\mathbb{Z}^{+}=\mathbb{N}=\{1,2,3,\dots\}$
Rational Numbers, $\mathbb{Q}$
$\mathbb{Q}=\left\{\frac{a}{b}\middle|a,b\in\mathbb{Z}, b\neq 0\right\}$
Irrational Set, $\mathbb{R}\setminus\mathbb{Q}$
$\mathbb{R}\setminus\mathbb{Q}=\{e,\pi,\sqrt{2},\dots\}$

Universal Quantifiers

in, $\in$
not in, $\notin$
such that, $\ni$
therefore, $\therefore$
because, $\because$
exist, $\exists$
for all, $\forall$
divides, $|$
does not divide, $\nmid$
implies, $\Rightarrow$
If and only if (iff), $\Leftrightarrow$
Modulo or Equivalent, $\equiv$
Goes to, $\to$
Subset, $\subset$
Tilda, $\sim$

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Number Set Notations & Universal Quantifiers

Number Set Notations

Universal Quantifiers

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