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

[Femme_physics]

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)?

 

[lurflurf]

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.

 

[ashishsinghal]

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

 

[Femme_physics]

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 :)

 

[deluks917]

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