Maximum

Ryan$

Junior Member
Joined
Jan 25, 2019
Messages
146
Hi guys; I know maybe it's trivial for others but for me still alil confused ..

the function max is giving me the maximum number of the numbers in other words max(4,5) = 5 ; but what's confusing me is max(5,5)=5 why? whenever the values of the elements of max are equal I got confusion .. why max (5,5) is 5?! maybe I defined the "max" in inappropriate way? can someone please instruct me about its definition(max definition) because every time I see the values are equal I get confused to find maximum of them ..



thanks!!
 

pka

Elite Member
Joined
Jan 29, 2005
Messages
7,818
the function max is giving me the maximum number of the numbers in other words max(4,5) = 5 ; but what's confusing me is max(5,5)=5 why? whenever the values of the elements of max are equal I got confusion .. why max (5,5) is 5?! maybe I defined the "max" in inappropriate way? can someone please instruct me about its definition(max definition) because every time I see the values are equal I get confused to find maximum of them .
As I read the question the fact that \(\displaystyle \max\{5,5\}=5\) is confusing for you.
Well \(\displaystyle \max\{y,x\}=\) the largest number that equals \(\displaystyle x\text{ or }y\) What is the largest number that equals \(\displaystyle 5\text{ or }5~?\)

Here is an interesting fact: if \(\displaystyle x>0~\&~y>0\) then \(\displaystyle \max\{x,~y\}=\dfrac{|x+y|+|x-y|}{2}\).
 

Denis

Senior Member
Joined
Feb 17, 2004
Messages
1,467
the function max is giving me the maximum number of the numbers in other words max(4,5) = 5 ; but what's confusing me is max(5,5)=5 why? whenever the values of the elements of max are equal I got confusion .. why max (5,5) is 5?! maybe I defined the "max" in inappropriate way? can someone please instruct me about its definition(max definition) because every time I see the values are equal I get confused to find maximum of them ..
Almost sounds as if you're joking!!
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
3,058
Hi guys; I know maybe it's trivial for others but for me still alil confused ..

the function max is giving me the maximum number of the numbers in other words max(4,5) = 5 ; but what's confusing me is max(5,5)=5 why? whenever the values of the elements of max are equal I got confusion .. why max (5,5) is 5?! maybe I defined the "max" in inappropriate way? can someone please instruct me about its definition(max definition) because every time I see the values are equal I get confused to find maximum of them ..

thanks!!
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!
 

Ryan$

Junior Member
Joined
Jan 25, 2019
Messages
146
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
Joined
Jan 29, 2005
Messages
7,818
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
Joined
Nov 12, 2017
Messages
3,058
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".
 
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