mjhjmtu

So I'm trying to have four different subsections on "2 different paragraphs". what I mean is the following:

 x ¦ x
 ----¦----
 x ¦ x

where x denotes the text I wish to have (without the dashed lines as there will be 4 sets of equations)

EDIT: This is what I've done thus far:

Let us define the following:

smallskip
$chi_0(x) = 1$
bigskip

$chi_1(x)$ = $begincases
 1, & textif x = 0, \
 a, & textif x = 1, \
 a^2, & textif x = 2, \
 a^3, & textif x = 3, \
 a^4, & textif x = 4, 
endcases$

$chi_2(x)$ = $begincases
 1, & textif x = 0, \
 a^2, & textif x = 1, \
 a^4, & textif x = 2, \
 a, & textif x = 3, \
 a^3, & textif x = 4, 
endcases$

$chi_3(x)$ = $begincases
 1, & textif x = 0, \
 a^3, & textif x = 1, \
 a, & textif x = 2, \
 a^4, & textif x = 3, \
 a^2, & textif x = 4, 
endcases$

$chi_4(x)$ = $begincases
 1, & textif x = 0, \
 a^4, & textif x = 1, \
 a^3, & textif x = 2, \
 a^2, & textif x = 3, \
 a, & textif x = 4, 
endcases$

Firstly I want to move the chi_0(x) down one line; and the other four "blocks" I want them to appear side by side like the following:

 chi_1(x) ¦ chi_3(x)
 ----------¦---------
 chi_2(x) ¦ chi_4(x)

I am unsure how to proceed.

The words "subsections" and "paragraphs" are here quite misleading because in TeX they refer to text elements, while you are writing equations. This might be a possible realization (I'm not sure where chi_0 is supposed to be)

documentclassarticle

usepackageamsmath

begindocument

beginalign*
chi_0(x) &= 1 \[1ex]
chi_1(x) &=
begincases
 1, & textif x = 0, \
 a, & textif x = 1, \
 a^2, & textif x = 2, \
 a^3, & textif x = 3, \
 a^4, & textif x = 4, 
endcases
&
chi_3(x) &=
begincases
 1, & textif x = 0, \
 a^3, & textif x = 1, \
 a, & textif x = 2, \
 a^4, & textif x = 3, \
 a^2, & textif x = 4, 
endcases
\[1ex]
chi_2(x) &=
begincases
 1, & textif x = 0, \
 a^2, & textif x = 1, \
 a^4, & textif x = 2, \
 a, & textif x = 3, \
 a^3, & textif x = 4, 
endcases
&
chi_4(x) &=
begincases
 1, & textif x = 0, \
 a^4, & textif x = 1, \
 a^3, & textif x = 2, \
 a^2, & textif x = 3, \
 a, & textif x = 4.
endcases
endalign*

enddocument

As campa stated, first showed question without code was misleading, and in this case can be nicely solved with align* (+1).

So this answer is not to search the acceptance, but just to show what you can with the commented minipages in other cases, not only with maths, since the minipages can contain anything, even a true subsection (e.g. subsectiontext Text ...) with images, tables, etc. But of course, also is possible only with your equations:

documentclass[12pt]article
usepackageamsmath
begindocument

Let us define the following:


[chi_0(x) = 1]

noindent
beginminipage[t].45textwidth
$chi_1(x)$ = $begincases
 1, & textif x = 0, \
 a, & textif x = 1, \
 a^2, & textif x = 2, \
 a^3, & textif x = 3, \
 a^4, & textif x = 4, 
endcases$bigskip
endminipagehfill%
beginminipage[t].45textwidth
$chi_3(x)$ = $begincases
 1, & textif x = 0, \
 a^3, & textif x = 1, \
 a, & textif x = 2, \
 a^4, & textif x = 3, \
 a^2, & textif x = 4, 
endcases$bigskip
endminipagehfill%
beginminipage[t].45textwidth
$chi_2(x)$ = $begincases
 1, & textif x = 0, \
 a^2, & textif x = 1, \
 a^4, & textif x = 2, \
 a, & textif x = 3, \
 a^3, & textif x = 4, 
endcases$bigskip
endminipagehfill%
beginminipage[t].45textwidth
$chi_4(x)$ = $begincases
 1, & textif x = 0, \
 a^4, & textif x = 1, \
 a^3, & textif x = 2, \
 a^2, & textif x = 3, \
 a, & textif x = 4, 
endcases$bigskip
endminipagehfill%

enddocument