Symbols and Jargon#
Glossary. Let me know what I’ve missed.
- \(\land\)#
Logical AND. \(a \land b\) means \(a\) is true AND \(b\) is true
- \(\lor\)#
Logical OR. \(a \lor b\) means \(a\) is true OR \(b\) is true (or possibly both)
- \(\implies\)#
Logical implication. \(a \implies b\) means IF \(a\) is true THEN \(b\) is true (anything can happen if \(a\) is false)
- \(\iff\)#
If and only if. \(a \iff b\) means \(a \implies b \land b \implies a\), i.e. \(a\) and \(b\) are equivalent.
- \(\forall\)#
For all … For example, \(\forall x \in \mathbb{N}, x < x + 1\) just says every \(x\) is less than \(x + 1\) (which is true)
- \(\exists\)#
There exists… For example, \(\exists x \in \mathbb{N}, x = x + 1\) just says there is some number \(x\) such that \(x = x + 1\) (which is false)
- \(\sum\)#
The sum of the whatever comes after. For example \(\sum_{i=1}^5 i^2 = 1^2 + 2^2 + 3^2 + 4^2 + 5^2\)
- \(\prod\)#
The product of whatever comes after. For example, \(\prod_{i=1}^5 i^2 = 1^2 \times 2^2 \times 3^2 \times 4^2 \times 5^2\)
- Set#
Just a bunch of stuff written between \(\{\) and \(\}\). See this section for more info.
- Function#
Mapping between sets, written \(f: A \to B\). See this section for more info.
- Bijection#
A special type of function \(f: A \to B\) in which pairs every element of \(B\) with exactly one element of \(A\).
- Number#
Amounty thing.
- Additive Number#
Numbers from the perspective of \(+\).
- Multiplicative Number#
Numbers from the perspective of \(\times\).
- Productive Number#
Numbers from the perspective of \(\prod_i p_i^{x_i}\) (\(p_i\) is ith prime).
- Factorization#
Breaking a number down into its prime exponents.
- Partial Order#
A way of comparing stuff \(x \leq y\) with fairly general requirements. See here.
- Total Order#
Partial order where everything is comparable.