Typo in Real Analysis Study Page: Absolute Value of x for x<0?

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Discussion Overview

The discussion revolves around the definition of the absolute value of a number, specifically for the case when x is less than 0. Participants are examining a study page in the context of real analysis and questioning whether the notation used is correct or if it represents a typo.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant suggests that the notation listing the absolute value of x for x<0 as -x may be a typo.
  • Another participant asserts that the definition of absolute value is standard, stating |x| = x if x>=0 and -x if x<0.
  • A participant expresses confusion about the notation, initially believing that absolute value should always be a positive number, referencing Wikipedia for clarification.
  • A later reply clarifies that the notation is indeed indicating the reversal of the sign for negative numbers, providing an example with x = -5 to illustrate that |x| = 5 corresponds to -x.

Areas of Agreement / Disagreement

There is no consensus on whether the notation is a typo or standard; participants express differing views on the clarity and correctness of the notation used in the study page.

Contextual Notes

Some participants reference external sources like Wikipedia, indicating that there may be varying interpretations of the absolute value concept and its notation.

starkind
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I found a study page which lists the absolute value of x for x<0 as -x. I think this has to be a typo. The study area is real analysis. Does anyone have better information? Maybe it is some special notation?
 
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I'm pretty sure this is the standard definition.

|x| = x if x>=0 and -x if x<0
 
Ouch. I thought absolute value was a difference expressed as a positive number.

I see in wikipedia that an absolute value is always positive. But the notation seems to indicate otherwise. What gives?

arghh. I see it now. The notation is saying to reverse the sign of a negative number. Thanks
 
Last edited:
starkind said:
Ouch. I thought absolute value was a difference expressed as a positive number.

I see in wikipedia that an absolute value is always positive. But the notation seems to indicate otherwise. What gives?

arghh. I see it now. The notation is saying to reverse the sign of a negative number. Thanks

It is. If x < 0 say x = -5 then you would want the |x| = 5 which is -x.
 

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