Main Content

Define less than relation

Use `assume`

and the relational operator
`<`

to set the assumption that `x`

is less than
3:

syms x assume(x < 3)

Solve this equation. The solver takes into account the assumption on variable
`x`

, and therefore returns these two solutions.

solve((x - 1)*(x - 2)*(x - 3)*(x - 4) == 0, x)

ans = 1 2

Use the relational operator `<`

to set this
condition on variable `x`

:

syms x cond = abs(sin(x)) + abs(cos(x)) < 6/5;

Use the `for`

loop with step *π*/24 to
find angles from 0 to *π* that satisfy that
condition:

for i = 0:sym(pi/24):sym(pi) if subs(cond, x, i) disp(i) end end

0 pi/24 (11*pi)/24 pi/2 (13*pi)/24 (23*pi)/24 pi

Calling

`<`

or`lt`

for non-symbolic`A`

and`B`

invokes the MATLAB^{®}`lt`

function. This function returns a logical array with elements set to logical`1 (true)`

where`A`

is less than`B`

; otherwise, it returns logical`0 (false)`

.If both

`A`

and`B`

are arrays, then these arrays must have the same dimensions.`A < B`

returns an array of relations`A(i,j,...) < B(i,j,...)`

If one input is scalar and the other an array, then the scalar input is expanded into an array of the same dimensions as the other array. In other words, if

`A`

is a variable (for example,`x`

), and`B`

is an*m*-by-*n*matrix, then`A`

is expanded into*m*-by-*n*matrix of elements, each set to`x`

.The field of complex numbers is not an ordered field. MATLAB projects complex numbers in relations to a real axis. For example,

`x < i`

becomes`x < 0`

, and`x < 3 + 2*i`

becomes`x < 3`

.