element of Z

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carebear

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I am learning Synthetic Division and in the textbook I am using it says:

Synthetic division can be used to divide a polynomial by a binomial of the x - a , a is an element of Z.

What is Z? I have heard of Natural Numbers (N), Whole Numbers (W), Integers(I), Rational Numbers (Q), Irrational Numbers (Q') and Real Numbers (R) but have never heard of Z......
 
carebear said:
I am learning Synthetic Division and in the textbook I am using it says:
Synthetic division can be used to divide a polynomial by a binomial of the x - a , a is an element of Z. What is Z?
Click to expand...
The symbol is usually \(\displaystyle \mathbb{Z}\), the first letter of the German word zahlen which means to count. Thus is stands for the set of integers \(\displaystyle \{0,~\pm 1,~\pm 2,\cdots\}\)
 
Denis said:
Z Z Z... means you're sleeping ;)

During pka's lecture!
Click to expand...

Not to be picky, but I think that the German word is the noun Zahl (number), instead of the verb zahlen (to count). After all, we count things with the numbers 1, 2, 3, et cetera; which is why the Natural numbers are also referred to as the set of counting numbers.

(I cannot remember seeing any symbol for the set of Irrationals.)
 
Now, \(\displaystyle \mathbb{I}\)'ve seen \(\displaystyle \mathbb{I}\)t all. :D
 
mmm4444bot said:
Not to be picky, but I think that the German word is the noun Zahl (number), instead of the verb zahlen (to count). After all, we count things with the numbers 1, 2, 3, et cetera; which is why the Natural numbers are also referred to as the set of counting numbers.
Click to expand...
Here is why that objection is completely wrong.
In German if one says, "let me count the ways..." the word zallen would be used. In other words, Germans would say, "let me number the ways"
In the German mind counting can be zero, positive, or negative.

Therefore, zalhen means to number and is translated as ​counted.
 
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