How is the notation $\{ \, . \} $ read in Mathematics I come across these notations often, I was wondering, how do you read them?
For instance, $\left\{ x \right\}$ where $\left\{ \, . \right\}$ denotes the fractional part function.
So. how do I read $\left\{ \, . \right\}$?
Another example, 
$ y = e^{2x+1} $ So the argument of $ e^{(  .  )} $ is $2x + 1$ again, how do I read the $( \, . )$
Thanks
 A: There are two issues. In your first example, the braces are one kind of grouping symbol and do not usually represent a mathematical object itself. Counterexamples are usually abuse of notation. For example, $\, (n,m) \,$ is often used to denote the greatest common divisor of $\,n\,$ and $\,m.\,$ However it is standard to use $\, \{n,m\} \,$ to denote the set with elements $\,n\,$ and $\,m.\,$ My preference would be to use "For instance, x wrapped in braces where braces denote the fractional part function." There are other ways to say the same thing.
In your second example, there is a use of positioning to represent a hidden and unnamed function. In this case, the power function. For historical reasons the logarithm function $\, \log_b(x) \,$ is explictly named while the inverse function $\, \textrm{pow}_b(x) := b^x \,$ is not. Also, for historical reasons the function $\, \exp(x) = e^x \,$ is singled out. My preference would be to simply use "y equals e raised to the power 2x plus 1." This seems clear and simple to me, but there are other ways to say the same thing.
