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What are the differences and common points between a variable and an indeterminate ? Is an indeterminate also a variable ?

Thank you

EDIT : I am not trying to solve anything in particular, it was just by reading the definition of both on Wikipedia and wanted some direct comparison. From what I understand, indeterminate enables you to compare two expressions directly while with a variable you would have to care about the values x might take...

Pop Flamingo
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  • That may depend on the context. Can you provide some examples of each? – Matthew Leingang May 10 '16 at 17:31
  • @MatthewLeingang I am not trying to solve anything in particular, it was just by reading the definition of both on Wikipedia and wanted some direct comparison of both. From what I understand, indeterminate enables you to compare two expressions directly while with a variable you would have to care about the values x might take... – Pop Flamingo May 10 '16 at 17:37
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    I think my usage falls along these lines: an indeterminate or unknown is a single value, while a variable stands for a range of values. – Matthew Leingang May 10 '16 at 17:40
  • @MatthewLeingang Do we ever have to specify for instance, to what set the indeterminate belongs to ? For instance aX² + bX + c couldn't be considered as a polynomial if we didn't specify that X belonged to the set of the real numbers would it ? – Pop Flamingo May 10 '16 at 17:44
  • Hm, I don't think I can cut it as cleanly as that. – Matthew Leingang May 10 '16 at 18:07
  • @MatthewLeingang Sorry I am not a native English speaker, what do you mean by "cut it as cleanly as that" ? – Pop Flamingo May 10 '16 at 18:10
  • @MatthewLeingang Actually, to my surprise, the wikipedia article says the exact opposite. A variable stands for something specific whereas an indeterminate would be used in a polynomial as a "place-holder" and not a "parameter of a problem". I think the gyst x is it's contextual and hierarchical. All indeterminates are variables but a variable is called an indeterminate if it isn't meant to take a specific value but to represent an abstract range of values. Example..... – fleablood May 10 '16 at 18:46
  • .... If we say 5x + 2 = 3x + 6 we are told there is a specific value that makes this true. A "determined" value. But when we say "5x + 2 and 3x + 5 are different linear equations; 5x + 2 \ne 3x + 6" we are not saying 5x+2 can not equal 3x +6 and therefore x can never equal 2-- we are saying the polynomials for x in general, for indeterminate values of x $5x + 2 \ne 3x + 6$. I wouldn't worry too much about it but if you need a simple definition I'd say: variables are unspecified quantities; indeterminate variables are not meant to have specific values. – fleablood May 10 '16 at 18:51
  • @fleablood Ok thank you I think I understand it better now, so when we say (in the wiki article) that when working in module 2 system, while x-x² = 0, X-X² is not the zero polynomial, is it because X-X² might be something like 1-0² ? – Pop Flamingo May 10 '16 at 18:56
  • Also, do we specify to what set the indeterminate belongs to ? – Pop Flamingo May 10 '16 at 18:57
  • To be honest, I've gone my entire life without giving much thought to the difference between the terms and use them mostly interchangibly. You should specify to what sets variables and indeterminates belong but that doesn't have anything to do with the definition. I think what wiki means to say is the value of $x - x^2$ is always 0 but that doesn't mean the polynomial is the same thing as the value. The polynomial is a concept and even though it always evaluates to 0, it is a different concept than the concept of the value of 0. – fleablood May 10 '16 at 19:11
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    Hello, your question has been asked here and actually got answers this time. Cheers – Caleb Stanford Sep 15 '16 at 05:44

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