lt

Define less than relation

In previous releases, `lt` in some cases evaluated inequalities involving only symbolic numbers and returned logical `1` or `0`. To obtain the same results as in previous releases, wrap inequalities in `isAlways`. For example, use `isAlways(A < B)`.

Syntax

`A < Blt(A,B)`

Description

`A < B` creates a less than relation.

`lt(A,B)` is equivalent to `A < B`.

Input Arguments

 `A` Number (integer, rational, floating-point, complex, or symbolic), symbolic variable or expression, or array of numbers, symbolic variables or expressions. `B` Number (integer, rational, floating-point, complex, or symbolic), symbolic variable or expression, or array of numbers, symbolic variables or expressions.

Examples

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```

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Tips

• 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`.