Symbol for Integers: Z or I or both?

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The standardized symbol for integers is widely recognized as Z, derived from the German word "zahlen," meaning numbers. While some textbooks, like the Alberta MathPower 10 from 1998, may use I to represent integers, this is less common and often considered non-standard. In computer science, I or i is frequently used as an identifier for integer variables, but this does not apply to the mathematical representation of the set of integers. It is essential to define notation conventions in any mathematical text, as different authors may choose different symbols. Ultimately, regardless of the symbol used, clarity in communication is key.
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Homework Statement
Personal Question: Internet says the standardized math symbol for integers is ##\mathbb {Z}##. However, my Alberta MathPower 10 (Western Edition) textbook from 1998 says the symbol is I. I'm guessing the textbook is wrong? Or are both answers correct?
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Personal Question:

Internet says the standardized math symbol for integers is ## \mathbb {Z}##. However, my Alberta MathPower 10 (Western Edition) textbook from 1998 says the symbol is I. I'm guessing that textbook is wrong? Or are both answers correct?
 
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Astro said:
Homework Statement:: Personal Question: Internet says the standardized math symbol for integers is ##\mathbb {Z}##. However, my Alberta MathPower 10 (Western Edition) textbook from 1998 says the symbol is I. I'm guessing the textbook is wrong? Or are both answers correct?
Relevant Equations:: not applicable (see homework statement)

Personal Question:

Internet says the standardized math symbol for integers is ## \mathbb {Z}##. However, my Alberta MathPower 10 (Western Edition) textbook from 1998 says the symbol is I. I'm guessing that textbook is wrong? Or are both answers correct?
I've never seen I used to represent the set of integers in any textbook. Instead, I've seen only ##\mathbb Z## used for this purpose. It comes from the German zahlen, (numbers).
 
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I've seen them both used (I don't remember if in books or articles). They are both acceptable. There is no mathematics enforcement police squad that needs to be satisfied. It is necessary to carefully define any notation conventions that will be used in a book or document, whether they are standard or not.
 
"I" or "i" is popular in CS circles ; blame Fortran, with its default of i-thru-n field names standing for type integers.
 
hmmm27 said:
"I" or "i" is popular in CS circles ; blame Fortran, with its default of i-thru-n field names standing for type integers.
But these are just identifiers for integer variables, not symbols that represent the set of integers, which is the topic at hand in this thread.
 
It is just a matter of convention the author chose. Z is the standard, from my own personal experience, and I have seen I used for the set of all irrational numbers in one book.

Whats important that every time you see I in your book. You know that they are referring to the set of all integers. If you may use another book, they may use the Z notation. For more advance books, it is important to read the first pages, to see what notation the author uses.
 
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Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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