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### Course: Algebra (all content)>Unit 7

Lesson 30: Two-variable functions

# New operator definitions 1

Sal solves a few problems where a new operator is defined and Sal evaluates some expression with it. Created by Sal Khan.

## Want to join the conversation?

• Are the symbols just like variables, but operations?
• Yes. Think of them as like the f in f(x), the sin in sin(x), the ! in x!, the + in x+y, the √ in √2, and many more things, but defined via operator.
(1 vote)
• Can you use symbols like a these? \$ % & € £ ¥ ₩ @ #
Or even a drawing?
• Definitely! You can use any symbols that you like or create your own. But to avoid confusion, it's not recommended to use signs, which have already a meaning like #, that has several meaning in mathematics ( cardinality in set theory, primorial in number theory and etc.)
• What does "⊘" mean??
• ø typically means the empty set, in set theory. However, you are probably using it to denote a "new operation".
Hope this helps!
• What is the difference between defining an operator and simply defining a function?
• + and - are actually forms of operators. So at some point they were defined. And f( ) is an operator. It is what you use to say "now use this function"
• What does diamond or star mean .
• it is just a defined operation.
for example # = multiplication
• Is it possible to define an order of operations precedence for operators you define?
• Yes. You can make operators anything you want.
(1 vote)
• so are the star and diamond there instead of an adding, subtracting, multiplying, or dividing symbol?
• No. a Star and a Dimond are absolutly NEW operations:not +.-.х,/.
Look here:
someone TOLD you that 3+4=7. I bet you have never asked why ! Well Sal here tries to explain:
that Dude, who told you that + sign works the way you know, told you this because SOME OTHER dude(the inventor) DEFIEND + sign to do this things, but the inventor of + sign could have invented a STAR(*), for example, IF he NEEDED it. Why he would need a STAR operator? Well, maybe he likede the idea that 3 * 4 would equal 34. Maybe Its good for inventing a warpdrive !:) who knows... You are free to invent your own operators!!!