What is [2x] Notation? Continuity Question

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Discussion Overview

The discussion revolves around the notation [2x] in the context of determining the continuity of a piecewise function. Participants explore the meaning of this notation and its implications for the function's behavior within the specified intervals.

Discussion Character

  • Conceptual clarification, Technical explanation

Main Points Raised

  • Some participants express confusion regarding the notation [2x] and its definition, noting a lack of information in their textbook and lectures.
  • One participant clarifies that the [x] notation refers to the floor function, which rounds down to the nearest integer below x.
  • Another participant confirms that for values like 1.2, the floor function yields a result of 1.

Areas of Agreement / Disagreement

There is a general agreement on the interpretation of the [x] notation as the floor function, but the initial confusion about its meaning indicates some uncertainty among participants.

Contextual Notes

Participants do not address potential limitations or assumptions regarding the continuity of the function itself, focusing instead on the notation.

FallArk
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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
 

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FallArk said:
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.
 
I like Serena said:
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?
 
FallArk said:
Then if i get 1.2, the result would be 1?

Yes.
$$[1] = [1.2] = [1.99] = 1$$
 

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