MHB What is [2x] Notation? Continuity Question

[FallArk]

The question asks me to determine whether the function is continuous?
f(x)=1, x =0,1
f(x)=x+[2x], 0<x<1
what is this [2x]? I cannot find it in the textbook and during lecture we had no information given about this.View attachment 6413

 

[I like Serena]

The question asks me to determine whether the function is continuous?
f(x)=1, x =0,1
f(x)=x+[2x], 0<x<1
what is this [2x]? I cannot find it in the textbook and during lecture we had no information given about this.

Hi FallArk!

The $[x]$ notation indicates the floor function.
That is, rounding down to the nearest integer below $x$.
Btw, I prefer the notation $\lfloor x \rfloor$, which is more intuitive.

 

[FallArk]

Hi FallArk!

The $[x]$ notation indicates the floor function.
That is, rounding down to the nearest integer below $x$.
Btw, I prefer the notation $\lfloor x \rfloor$, which is more intuitive.

Then if i get 1.2, the result would be 1?

 

[I like Serena]

Then if i get 1.2, the result would be 1?

Yes.
$$[1] = [1.2] = [1.99] = 1$$