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

• starkind
In summary, The conversation discusses the definition of absolute value and the notation used to represent it. There is confusion about the notation, but it is clarified that the notation is simply indicating to reverse the sign of a negative number. The standard definition of absolute value is |x| = x if x>=0 and -x if x<0.
starkind
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?

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.

## 1. What is a typo in real analysis?

A typo in real analysis is a mistake or error in a mathematical proof or statement that can change the meaning or validity of the argument. Typos are common in mathematics and can be caused by simple mistakes in calculations, forgetting to include a step, or misinterpreting symbols or notation.

## 2. What does the absolute value of x for x<0 mean?

The absolute value of x for x<0 is a mathematical expression that represents the distance of a number from zero on a number line. When x is less than zero, the absolute value of x is equal to x multiplied by -1, so it essentially "flips" the negative sign to make the number positive.

## 3. How do typos impact real analysis studies?

Typos can have a significant impact on real analysis studies, as they can lead to incorrect proofs and conclusions. Inaccurate results can then be applied to further mathematical concepts, causing a chain reaction of incorrect information. It is important for mathematicians and scientists to carefully check for typos and correct them to ensure the validity of their work.

## 4. Why is the absolute value of x for x<0 important in real analysis?

The absolute value of x for x<0 is important in real analysis because it allows for the consideration of both positive and negative numbers in mathematical equations. It also helps to define the concept of distance and plays a crucial role in the study of limits, continuity, and differentiation.

## 5. How can one avoid typos in real analysis studies?

To avoid typos in real analysis studies, it is important to carefully check all calculations and proofs, double-check notation and symbols, and have another person review the work for any potential errors. It is also helpful to use computer software or calculators to assist in calculations and to have a strong understanding of mathematical concepts and notation.

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