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

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Discussion Overview

The discussion revolves around the definition and significance of the binary operator $\oplus$, specifically defined as $a \oplus b = 4ab$. Participants explore its application through examples and question its relevance in various mathematical contexts.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants define the binary operator $\oplus$ as $a \oplus b = 4ab$ and provide calculations for specific values.
  • There is a suggestion that the significance of $\oplus$ may vary depending on the context of the problem, as noted by one participant.
  • Some participants express uncertainty about the operator's relevance, indicating they have not encountered it in their studies.
  • Another participant mentions that binary operations can be found in various contexts where relations are discussed.

Areas of Agreement / Disagreement

Participants generally agree on the definition of the operator but express differing levels of familiarity and understanding regarding its significance and applications.

Contextual Notes

Some participants note a lack of exposure to the concept in their educational experiences, suggesting that its relevance may depend on specific mathematical contexts or courses.

karush
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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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