# Clarification/correction in Volume V, Chapter 4, Basic Identities

#### Mark44

Joined Nov 26, 2007
628
[Copied from topic]Note: while division by zero is popularly thought to be equal to infinity, this is not technically true. In some practical applications it may be helpful to think the result of such a fraction approaching infinity as the denominator approaches zero (imagine calculating current I=E/R in a circuit with resistance approaching zero -- current would approach infinity), but the actual fraction of anything divided by zero is undefined in the scope of "real" numbers.
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It's not even technically true if you allow for negative denominators that are close to zero. Assuming a positive numerator and a positive denominator, the value of the fraction increases without bound (approaches infinity) as the denominator approaches zero. If the denominator is negative, however, the value of the fraction decreases without bound (approaches negative infinity) as the denominator approaches zero. These can be stated much more succinctly using one-sided limit notation.

Quotes aren't needed around real in "real" numbers. Division by zero is also undefined for complex numbers.

#### Dcrunkilton

Joined Jul 31, 2004
422
[Copied from topic]Note: while division by zero is popularly thought to be equal to infinity, this is not technically true. In some practical applications it may be helpful to think the result of such a fraction approaching infinity as the denominator approaches zero (imagine calculating current I=E/R in a circuit with resistance approaching zero -- current would approach infinity), but the actual fraction of anything divided by zero is undefined in the scope of "real" numbers.
[End of copied material]

It's not even technically true if you allow for negative denominators that are close to zero. Assuming a positive numerator and a positive denominator, the value of the fraction increases without bound (approaches infinity) as the denominator approaches zero. If the denominator is negative, however, the value of the fraction decreases without bound (approaches negative infinity) as the denominator approaches zero. These can be stated much more succinctly using one-sided limit notation.

Quotes aren't needed around real in "real" numbers. Division by zero is also undefined for complex numbers.

Thanks for the suggestion Mark44. Here is my proposed change to the text.

[Copied from topic, proposed change]Note: while division by zero is popularly thought to be equal to infinity, this is not technically true. In some practical applications it may be helpful to think the result of such a fraction approaching positive infinity as a positive denominator approaches zero (imagine calculating current I=E/R in a circuit with resistance approaching zero -- current would approach infinity), but the actual fraction of anything divided by zero is undefined in the scope of either real or complex numbers.
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However, I need at least one other opinion on this before making a change to the master copy.

#### Dave

Joined Nov 17, 2003
6,969
Thanks for the suggestion Mark44. Here is my proposed change to the text.

[Copied from topic, proposed change]Note: while division by zero is popularly thought to be equal to infinity, this is not technically true. In some practical applications it may be helpful to think the result of such a fraction approaching positive infinity as a positive denominator approaches zero (imagine calculating current I=E/R in a circuit with resistance approaching zero -- current would approach infinity), but the actual fraction of anything divided by zero is undefined in the scope of either real or complex numbers.
[End of copied material, proposed change]

However, I need at least one other opinion on this before making a change to the master copy.
I concur with the suggestions put forward by Mark44. The corrections reflect the suggestions in his comments and I think are both accurate and applicable in the context of applications where this e-book is focused.

Dave

#### Mark44

Joined Nov 26, 2007
628
Looks good.

#### Dcrunkilton

Joined Jul 31, 2004
422
Thanks for all the help. The changes have been made at ibiblio.