What's the actual difference between undefined and indeterminate form ?

In summary, the difference between "undefined" and "indeterminate form" is that undefined means the limit does not exist, while indeterminate form means that further analysis is required to determine the limit. 0/0 is considered an indeterminate form, while something over 0 is considered undefined. This is because when finding limits, a superficial analysis is often performed and division by zero is permissible in an extended number system. However, in some cases, this analysis is inconclusive and further work is needed to determine the limit.
  • #1
Femme_physics
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What's the actual difference between "undefined" and "indeterminate form"?

As per the attachment, I understand that 0 over 0 is indeterminate form, and that something over 0 is undefined. The fact these 2 math expressions have 2 different words describing them doesn't actually tell me their difference. Aren't they both considered a "meaningless expression" (undefined and indeterminate form)?
 

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  • #2


I assume you are talking about finding limits. When finding limits one often does a sort of superficial analysis. Often this analysis is preformed in an extended number system in which division by zero is permissible. As per your attachment sometimes this analysis is conclusive and sometimes further analysis is required. If we say a limit is undefined we mean that is does not exist; sometimes we also like to remark as to why for example diverges to infinity, diverges to minus infinity, or oscillates. When we say a limit is of a particular indeterminate form such as 0/0,0*infinity,infinity/infinity,1^infinity,0^0 or some other; we mean that our simple analysis has failed and we make no conclusion based on it. That is the limit may exist or it may not.
 
  • #3


Femme_physics said:
I understand that 0 over 0 is indeterminate form, and that something over 0 is undefined.


actually tending to zero over tending to zero is called indeterminate form. for eg
x-2/x-2 is not defined at x = 2. but if x is not equal to zero but very close to it
ie

x = 1.999999999999... then x-2/x-2 = 1
this is called x tends to 2 (but is not equal to it)

when we have 0/0 form in limiting case - we convert it into something that is determinate and we finally give its value
 
  • #4


Ah, I see, so 0/0 just means that the limit exists it just needs more work finding it out, whereas a number over 0 means it doesn't exist!

Thanks :)
 
  • #5


0/0 is more like might exist but yo get the idea.
 

What is the difference between undefined and indeterminate form?

The main difference between undefined and indeterminate form is that undefined refers to a mathematical expression that does not have a defined value, while indeterminate form refers to a limit that cannot be determined through the usual methods of algebraic manipulation.

How can I identify an undefined form in a mathematical expression?

An undefined form can be identified by looking for any mathematical operations that would result in a division by zero, such as dividing a number by 0 or taking the square root of a negative number.

What are some examples of undefined forms?

Some examples of undefined forms include 0/0, √(-1), and 1/0.

How can I identify an indeterminate form in a limit?

An indeterminate form in a limit can be identified by using the limit laws and algebraic manipulation to simplify the expression. If the limit still cannot be determined, then it is considered an indeterminate form.

What are some examples of indeterminate forms?

Some examples of indeterminate forms include 0/0, ∞/∞, and 0*∞.

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