[x]: what do the brackets mean, for instance, in "[tan-1(-1)]=" ?

[bobrossu]

What does it mean when something is surrounded by brackets? For example: [tan^-1(-1)]=?

I heard that it means the greatest integer, but what does that really mean?

Some explanation and examples would be nice as well as a solution to the given example. Thanks!

 

[ksdhart2]

What does it mean when something is surrounded by brackets? For example: [tan^-1(-1)]=?

I heard that it means the greatest integer, but what does that really mean?

Some explanation and examples would be nice as well as a solution to the given example. Thanks!

It can mean that, but it doesn't always. Most often, I see the square brackets simply used for nested grouping symbols. For instance, rather than 1 / (2 * (3 + 4)), you might see 1 / [2 * (3+4)], just to make a bit more clear which sets of grouping symbols belong where.

In the event that [x] does mean the greatest integer function (which may also be written as floor(x) or \(\displaystyle \lfloor x \rfloor\)), that function simply returns the greatest integer that is less than or equal to x. Another way of phrasing it is to say that you round down to the nearest integer. There is a counterpart to this function called the step function or ceiling(x) or ceil(x). Sometimes it is written as \(\displaystyle \lceil x \rceil\). That tells you to find the smallest integer greater than or equal to x. In other words, round up. Some examples of this:

\(\displaystyle \lfloor 5.7 \rfloor = 5\)

\(\displaystyle \lfloor 8.2 \rfloor = 8\)

\(\displaystyle \lceil 6.99 \rceil = 7\)

\(\displaystyle \lceil 1.267 \rceil = 2\)

 

[tkhunny]

Sometimes, it's just brackets.


{[(x + 2) - 5y] + 7z}

 

[JeffM]

What does it mean when something is surrounded by brackets? For example: [tan^-1(-1)]=?

I heard that it means the greatest integer, but what does that really mean?

Some explanation and examples would be nice as well as a solution to the given example. Thanks!

Actually the proper symbol for the largest integer component of a number is not square bracket, but this:

\(\displaystyle \lfloor 2.4 \rfloor = 2 = \lfloor 2.0 \rfloor.\)

And then there is this

\(\displaystyle \lceil 2.4 \rceil = 3 = \lceil 3.0 \rceil \)