Question 1208139
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Use set-builder notation to denote the set of all even digits.
Let me see.
Let E = set of even digits

(a) E = { x | x is an even digit } = { 0,2,4,6,8 }
(b) Why is 0 an element of set E?
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<pre>
(a) is correct;


(b) is by definition (since 0 is an even number).
</pre>


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<U>Comment from student</U>: How is zero (the absence of value) be an even number?



<U>My response</U>. It is a great mistake and a fatal error to think that zero is the absence of value.


In opposite, zero has a very specific value and expresses the absent of amount.



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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A typical example is when in your pocket 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;you do not have neither banknotes nor coins.


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When you divide zero by two in integer numbers, you obtain zero as the quotient and zero as the remainder.


It means that zero is an even number, in the row of other even integer numbers 
that are divisible by two with no remainder.



Usually/normally, students learn these truths/conceptions in the second or third grade.



As I see from your posts, you try to review College Algebra without having necessary 

elementary standard basic knowledge (prerequisites) related to the second and/or  third grade.



I just made similar notices two times before, responding to your preceding posts.



So, if you want to know my opinion, it is that you should not reviewing College Algebra,

but start from Arithmetic and then continue with Pre-Algebra.



It will better correspond to your current level in Math.