Question 1208147: The set of digits consists of the following set of numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
The textbook tells me that we can denote the set of digits using a Roster Method.
Let D = set of digits
D = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
The book goes on to say that there is a second way to denote a set. That is to use set-builder notation, where the set D of digits is written as D = { x | x is a digit }.
Questions
1. Use the Roster Method to denote the set of even digits.
Let E = set of even digits.
Textbook answer: E = { 0, 2, 4, 6, 8 }.
Why is 0 an element of set E? I thought the whole number 0 is a number without value.
2. Use Set-builder Notation to denote the set of odd digits.
Let O = set of odd digits.
0 = { x | x is an odd digits} = { 1, 3, 5, 7, 9 }
You say?
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! .
(2) is close to be correct, but is not fully correct.
In order for (2) be fully correct, it should be written in the form
O = { x | x is an odd digits} = { 1, 3, 5, 7, 9 },
where symbol O in the left side is letter O (not digit "0", meaning zero).
(1) Textbook answer E = { 0, 2, 4, 6, 8 } is correct.
0 is an even digit.
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Question from student: Why is 0 an element of set E? I thought the whole number 0 is a number without value.
My response. 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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A typical example is when in your pocket
you have neither banknotes nor coins.
Then you say that the amount of cash in your pocket is zero.
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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 this truth/conception 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 three 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.
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