Braces are marks used to group operations and mark the beginning and end of sets. Braces are always used in pairs. The left brace looks like: {. The right brace looks like: }.
Braces are most often used to mark the beginning and end of sets in set notation. For example: A = {x|x>5}.
Braces are occasionally used to group operations in arithmetic, usually along with parentheses. For example, the expression 5·4+2 evaluates to 22. Using the order of operations, we first multiply 5 and 4 to get 20, and then add 2 to get 22.
However, if we use braces write the expression as 5·{4+2}, the value of the expression changes. The brace tells us to add 4 to 2 before multiplying by 5. Adding 4 and 2 gives us 6. When we then multiply by 5 we get 30.
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