User:JimColes/sandbox

= Jim Coles's Sandbox =

Put thoughts and knowledge here, Jimbo.

Math Formulas using LaTex
Accents and diacritics: $$\tilde{a}, \ddot{a}, \vec{a}, \breve{a}, \acute{a}$$

Symbols and constants: $$\infty, \Re, \circledS, (more)$$

Foundations
Sets: $$\bigcap_{x}^{y} \bigcup \{ \} \in \varnothing$$ (many more)

Basic Operators: $$+, -, \times, \div, /, \cdot$$

Advanced Operators: $$\pm, \mp, \dotplus, \divideontimes, \backslash, \circ, \bullet, \boxplus, \boxminus, \boxtimes, \boxdot, \oplus, \ominus, \oslash, \odot, \circleddash, \circledcirc, \circledast \bigoplus_{x}^{y}, \bigotimes, \bigodot$$

$$ \bigoplus$$$$ \bigotimes$$$$ \bigodot$$

Modulo Arithmetic: $$\pmod{m}, a\bmod b, \gcd(m, n), \operatorname{lcm}(m, n), \mid, \nmid, \shortmid, \nshortmid$$

Exponentials
Terms: $$base^{exponent} = power $$

The terms base may also be called radix or root.

So, 100 is a power of base 10 since $$10^{2} = 100 $$.

Exponential notation: $${x_2}^3 a^2 a^{2+2} {x_2}^3 x_2^3 10^{10^{8}} f' f'' $$

Radicals: $$\surd, \sqrt{2}, \sqrt[n]{2}$$

Standard Functions using general syntax: $$\exp_a, \log_{10}, \sin, \max(x,y)$$

Advanced Math
Differential and Integrals:$$\sum_{k=1}^N \sideset{_1^2}{_3^4} \prod_a^b \int_{}^{} \lim_{n \to \infty} \textstyle \lim_{n \to \infty} \displaystyle \int_{1}^{3} x \iiint xyz   \oint x \bigcup_{i=1}^n dy/dx {dy \over dx} {\partial^2\over\partial x_1\partial x_2}y f^{(3)} \ddot y $$

Relations: $$\equiv = \neq \not\equiv \doteq \doteqdot \overset{\underset{\mathrm{def}}{}}{=} \backsim > \geq \lesseqqgtr \succnapprox $$ (and many more)

Greek Alphabet
$$\Alpha \alpha \Beta \beta \Gamma \gamma \Delta \delta \Epsilon \epsilon \Zeta \zeta \Eta \eta \Theta \theta \Iota \iota \Kappa \kappa \Lambda \lambda \Mu \mu \Nu \nu \Xi \xi \Pi \pi \Rho \rho \Sigma \sigma \Tau \tau \Upsilon \upsilon \Phi \phi \Chi \chi \Psi \psi \Omega \omega \varepsilon \varpi \varrho \vartheta \varphi$$