MHB What is the Binary Operator $\oplus$ and its Significance?

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The binary operator $\oplus$ is defined as $a \oplus b = 4ab$, with examples showing its application, such as $9 \oplus 3 = 108$ and $2 \oplus 2 = 16$. The significance of $\oplus$ varies depending on the context, as binary operations can be relevant in many mathematical problems and relations. Participants express confusion over its simplicity and mention a lack of exposure to such concepts in their education. The discussion highlights that binary operations are foundational in understanding relations in mathematics. Overall, the operator's significance lies in its versatility across different mathematical contexts.
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define the binary operater $\oplus$ by
a$\oplus$b=4ab
find

a. $9\oplus 3$=4(9)(3)=108
b. $2\oplus 2$=4(2)(2)=16
c. $3\oplus 9$=4(3)(9)=108
d. $g\oplus h$=4(g)(h)=4gh

ok that was too simple must be doing something wrong

what is the significance lf $\oplus$
 
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karush said:
define the binary operater $\oplus$ by
a$\oplus$b=4ab
find

a. $9\oplus 3$=4(9)(3)=108
b. $2\oplus 2$=4(2)(2)=16
c. $3\oplus 9$=4(3)(9)=108
d. $g\oplus h$=4(g)(h)=4gh

ok that was too simple must be doing something wrong

what is the significance lf $\oplus$
Nope. It's that simple. As to the significance of [math]\oplus[/math] that depends on the context of the problem. Binary operations can be defined for many specific types of problems.

-Dan
 
ok i never saw this stuff in any class i took
not even sure what class its found in
 
karush said:
ok i never saw this stuff in any class i took
not even sure what class its found in
In one form or another you can find them anywhere relations are mentioned. A binary operation is an example of a relation.

-Dan
 

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