test.tex

\documentclass{article}   
\usepackage{amsmath, amssymb}
\begin{document}

$\forall x > 0(x^ax^b = x^{a+b})$

$\forall x > 0(x^ax^b = x^{a+b})$

$\forall x,y > 0((xy)^a = x^ay^a)$

$|x+y| \le |x|+|y|$

$|xy| = |x| |y|$

$(|xy| = |x|) |y|$

$x+y = y+x$

$(x+y)+z = x+(y+z)$

$x+0 = x$

$x+-x = 0$

$-x+x = 0$

$xyz = x(yz)$

$x(y+z) = xy+xz$

$(x+y)\cdot z = x\cdot z+y\cdot z$

$a|b \iff \exists c \in \mathbb Z (ac = b)$

$a\mid b \iff \exists c \in \mathbb Z (ac = b)$

$A\cup B = \{x \mid x \in A \lor x \in B\}$

$d/dxf(x) = \lim_{h\to 0} (f(x+h)-f(x))/h$

$d/dx(f(x)g(x)) = d/dxf(x)g(x)+f(x)d/dxg(x)$

$(f(g))' = f'g+(f(g))'$

$x+\cdot y$

$\int_a^bf(x)dx = \lim_{n\to \infty } (\sum_{i = 1}^nf(x_i^*)(b-a)/n)$

$\int f(x)dx = F(x)+C$

$\int_C f(x)dx = 0$

$\prod_{i = 1}^{n+1}a_i = (\prod_{i = 1}^na_i)a_{n+1}$

$\delta +1$

$\lim_{x\to a} f(x) = L \iff \forall \varepsilon  > 0\exists \delta  > 0\forall x(0 < |x-a| < \delta  \implies |f(x)-L| < \varepsilon )$

$\sin xy$

$\sin x+y$

$\sin x$

$f(x)y$

$a:A\times A\to A$

$A \models \varphi $

$1/2x$

$(1/2)\cdot x$

$f(x,y,z,u,v,w)$

$x R y \land y R z \implies x R z$

$f(x)^2$

$f^2x = f(x)^2$

$\sin ^2x$

$n:\mathbb N $

$f'x = (f(x))' = d/dxf(x)$

$\mathbb N  \subset \mathbb Z  \subset \mathbb Q  \subset \mathbb R  \subset \mathbb C $

$\lim f(x)$

$2(1+1) = -21.0$

$f[X] = \{f(x) \mid x \in X\}$

$((A\times A)\times A)\times A\to (A\to (A\to (A\to A)))$

$h:\mathbb R ^m\to \mathbb R ^n$

$(f+g)x$

$f,\dots ,g$

$f$

$\mbox{abso}(\vee ,\wedge ) = ((x\vee y)\wedge x = x)$

$\mbox{LatticeAx}(\vee ,\wedge ) = (\mbox{SemilatticeAx}(\vee ) \land \mbox{SemilatticeAx}(\wedge ) \land \mbox{abso}(\vee ,\wedge ) \land \mbox{abso}(\wedge ,\vee ))$

\end{document}