# 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

• This isn’t definitive, but for your second example, I might say “the argument of the exponential function is two ex plus one.” – David M. Jul 21 '18 at 12:46
• Well, how would you read $\{x\}$ in the first place? – Crosby Jul 21 '18 at 13:08
• @Crosby It's read as fractional part of $x$ – William Jul 21 '18 at 13:08
• @William I think it's rather meaningless to say this out loud; as mentioned, it's just a device to familiarize a reader with notation. If you insist, however, I would just say something like "$\{x\}$ where the brackets denote the fractional part of $x$." This is more relevant if you are explaining something you wrote on (say) a chalkboard, as then one does not necessarily have to pronounce $\{x\}$ before one has given its meaning. – Crosby Jul 21 '18 at 13:14
• We write things all the time that sound strange when read aloud. Writing: "Consider $\Gamma(5)$, where $\Gamma$ is the gamma function." Reading: "Consider gamma of $5$, where gamma is the gamma function." – GEdgar Jul 21 '18 at 15:04

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.
• This particular "power" function actually does have a name: the exponential function, sometimes denoted $\exp(\cdot).$ – David K Jul 21 '18 at 23:30