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Indeterminate / Indeterminate Form

 

The literal meaning of Indeterminate is 'something that cannot determined'. Why it cannot be determined ? Does it simply because I am not knowledgeable enough ? (i.e, due to lack of knowledge ?). No. it is not because of lack of knowledge nor because you didn't study enough. It is because it cannot be specified mathematically.

Like most of other mathematical concept, the definition of Indeterminate look short, but understanding real meaning of the definition is not easy (actually very difficult). If you don't understand the exact meaning of this just by reading the definition here, don't get frustrated. It is not only you who has the same problem.

If you are really interested in understanding the exact meaning of 'Indeterminate', search in the web around 10 different definitions from 10 different persons (or text books). I put some of the sources that I have found useful to me in the Reference section. Even if you do that, it is not guaranteed that you will have very clear understanding and describe the definition in your own words, but at least you will have some intuitive understanding in your brain.

If you don't want to spend such a time and effort to do this. It is OK.. for most of practical situation, it would be good enough to know that it usually mean following expression when we talk of 'Indeterminate (or Indeterminate expression)''.

 

 

Similary, you may heard people (or textbook) talk about 'Indeterminate Form'. In some cases, 'Indeterminate Form' would refer to the expressions listed above, but in many case 'Indeterminate Form' is mentioned in the context of 'Limit' operation.

 

 

Example 1 >

 

Is following an Indeterminate Expression ?

 

Yes. it is an indeterminate expression as shown below.

 

 

 

Example 2 >

 

Is following an Indeterminate Expression ?

 

Yes. it is an indeterminate expression as shown below.

 

 

 

Reference :

 

[1] Undefined vs Indeterminate in Mathematics

[2] Indeterminate Expression

[3] Indeterminate (Wolfram Mathworld)  

[4] Indeterminate forms(Roberto’s Notes on Differential Calculus)