# Maximum

##### Junior Member
You have a function "max" that gives the largest of its arguments; for instance, if you have two children who are 4 and 5 years old, respectively, then max(4, 5) tells you the age of the older one.

What it you had twins, both 5 years old? Doesn't it make sense that max(5, 5) should be 5, the age of the "older" one (namely, of either one)? In a sense, neither is older, so you could quibble about it; but what other answer would make sense?

A technical definition of max(x, y) would be "the smallest number that is no larger than either x or y". Once we have made such a definition, we don't need to worry about oddities in the English. That's one reason math is written using symbols rather than in English words!
so I can say that max is returning the largest number regardless to its elements(numbers) if they are equal or not .. doesn't matter what's matter "the largest" ye?

#### pka

##### Elite Member
so I can say that max is returning the largest number regardless to its elements(numbers) if they are equal or not .. doesn't matter what's matter "the largest" ye?
Your question is not clear. It is true that
1)$$\displaystyle \max\{x,y\}=\max\{y,x\}$$ order does not matter, $$\displaystyle \max\{-7,0\}=\max\{0,-7\}=0$$
2) Also and again $$\displaystyle \max\{6,6\}=6$$,
3) The arguments may be more than two $$\displaystyle \max\{8,6,-5,-7\}=8$$

#### Dr.Peterson

##### Elite Member
so I can say that max is returning the largest number regardless to its elements(numbers) if they are equal or not .. doesn't matter what's matter "the largest" ye?
Correct. The numbers don't have to be different; you are finding the largest value among them, not identifying one of them as "the largest".