# Maximum

(Redirected from Max)
 `⌈`

Maximum (`⌈`), Max, Greater of, or Larger of is a dyadic scalar function which returns the larger of its two arguments. The name "Maximum" is sometimes also used for the Maximum Reduce `⌈/`, which returns the largest element of a vector (this usage is related to the maximum of a function). Maximum is paired with Minimum, and shares the glyph `⌈` with the Ceiling function. It is not subject to comparison tolerance, since the result will be exactly equal to one argument, and there is no reason to choose a smaller argument even if the two arguments are tolerantly equal. As a Boolean function, Maximum is identical to Or.

## Examples

Maximum finds the larger of two numbers:

```      2.4 ⌈ 1.9
2.4```

Maximum Reduce finds the largest element in a vector:

```      ⌈/ 4 3 2 7 5 1 3
7```

The index of this element can be found with Index Of, but is also the First element of the Grade Down of the vector.

```      {⍵⍳⌈/⍵} 4 3 2 7 5 1 3
4
⊃⍒ 4 3 2 7 5 1 3
4```

Reducing over an empty axis yields the smallest representable number, as that is the identity element for Maximum. This value is usually `¯∞` (for dialects that support infinities) or `¯1.797693135E308` (with 64-bit floats) or `¯1E6145` (with 128-bit decimal floats).