Linear Algebra: Understanding max(x,y) in x \oplus y

[harvellt]

Not sure if this is the best place for this, its not an entire problem I am having trouble with but a small part of one.
I am working on linear algebra and I can't find a good explanation for
$$x \oplus y= max(x,y)$$

What or of max is it? Additive, multiplicative?

Thank you so much been trying to do my own research but can't seem to find it.

 

[Petek]

It looks like the author is defining a new operation $\oplus$ that is not either addition or multiplication. The result of applying $\oplus$ to two integers is, by definition, the greater of the two integers. Presumably, you are then asked to prove whether or not this operation satisfies certain properties (commutivity, associativity, etc.).

Does that help?

Petek

 

[harvellt]

yep exactly that is very helpful! So you think that $$max(1,2)=2$$? for example?
The full problem defines scalar multiplication normally and then gives that operation over Reals and asks if it is a vector space.

 

[Petek]

yep exactly that is very helpful! So you think that $$max(1,2)=2$$? for example?
The full problem defines scalar multiplication normally and then gives that operation over Reals and asks if it is a vector space.

Correct, so $1 \oplus 2 = 2$.

Petek

 

[HallsofIvy]

"Addtion" in a vector space has to satisfy:
1) Associative. Is $a\oplus(b\oplus c)= (a\oplus b)\oplus c$ for all numbers, a, b, and c?
2) Commutative. Is $a\oplus b= b\oplus c$?
3) Distributive. Is $a(b\oplus c)= ab\oplus ac$?
4) Additive identity. Is there some "e" such that \(\displaystyle a\oplus e= a\) for all a?
5) Additive inverses. For every number a, is there a number b such that a\oplus b= e, where e is as in (4)?

For example, $a\oplus(b\oplus c)= a\oplus max(b,c)$= max(a, max(b,c))= max(a,b,c).