Examples of Binary Operations (and Non-Examples) | Abstract Algebra

What are binary operations? A binary operation is a function from the cartesian product of a set with itself back to that same set. In other words, a binary operations takes two elements from the same set and assigns the ordered pair of them to exactly one element also in that set (since it always stays within the same set, a binary operation is "closed", and this closure is one of its most important properties). We'll see several examples of binary operations as well as relations that are not binary operations in today's abstract algebra lesson.

Thanks to Nasser Alhouti, Robert Rennie, Barbara Sharrock, and Lyndon for their generous support on Patreon!

I hope you find this video helpful, and be sure to ask any questions down in the comments!

+WRATH OF MATH+

Follow Wrath of Math on...

[MrCoreyTexas]

very interesting problem in the last half, never saw this before.

[LDB-czwf]

For the area of a rectangle example, can one argue that a rectangle is undefined for non-positive dimensions, hence the binary operation is undefined when one or more of L, W is nonpositive?

[joefuentes]

So when something isn't a binary operation then what do you call it? In the case of natural number subtraction? Or is there no name for it and technically we just need to specify that the number on the right be equal to or less than the left and then it's a binary operation?!?

Edit: I see "partial binary operation"... Is that correct?

[HaCkeMatician]

Hey!
Thanks for your great videos 👌👍
What are the prerequisites I need in order to study Abstract algebra ?

Thanks!

[sneedle]

What do we call operations that produce more than one result, e.g. the square root