# Undefined value and Infinite value

• salil87
In summary, undefined and infinite are not always interchangeable for functions. While infinite values often result in an undefined value, it is not always the case. For example, the function log(x) is undefined at zero but not infinite. Additionally, the concept of undefined does not always involve infinity, such as with the empty function or in cases where a function is defined only for certain values of x.
salil87
Hi
When we say that a function has an undefined value at a particular time does it mean it is infinite at that time? I mean most of the time it is infinite. But is an infinite value always called undefined and is an undefined value always infinite? If so why is it called undefined? Why not infinity?
Thanks
Salil

Welcome to PF, salil87!

Infinite and undefined are different things.
For a function, infinite usually implies undefined.
But undefined does not have to be infinite.

For instance, the function log(x) is negative infinity at zero and as such undefined at zero.
But for negative values of x, log(x) is simply undefined (but not infinite).

for a slighty silly example, consider the empty function, which has no domain.

its graph is, of course, blank, but infinity doesn't even enter the picture.

Or: define f(x)= 3x for x> 0, f(x)= 2x for x< 0. Then f(0) is, literally, "undefined".

Thanks a lot. :-)

Thanks
Salil

## What is an undefined value?

An undefined value is a value that is not defined or assigned to a variable. It could be the result of an error or a variable that has not been initialized.

## What is an infinite value?

An infinite value is a mathematical concept that represents a quantity that has no limit. This can be either positive or negative and can be expressed as ∞ or -∞.

## What is the difference between undefined and infinite values?

The main difference is that an undefined value has no value at all, while an infinite value has a value that has no limit. Undefined values are typically the result of an error, while infinite values are used in calculations and represent a concept of endlessness.

## Can undefined or infinite values be used in calculations?

Yes, both undefined and infinite values can be used in calculations, but they may result in unexpected outcomes. It is important to handle these values appropriately in order to avoid errors in calculations.

## How can undefined or infinite values be handled in programming?

Undefined values can be handled by checking for errors and properly assigning values to variables. Infinite values can be handled by setting a limit or using conditional statements to prevent endless loops in calculations.

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