Question 1197897: Given that set E = {x | x is an even digit }, use the Roster Method to show the even digits requested.
According to the textbook author, the answer is E = {0, 2, 4, 6, 8}.
My question is about 0. Is zero an even digit? Why is 0 on that list of even digits for set E?
Found 2 solutions by math_tutor2020, math_helper:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
An even number is anything that is a multiple of 2.
More formally, it's a number of the form 2k where k is an integer.
set of integers = {..., -3, -2, -1, 0, 1, 2, 3, ...}
i.e. set of positive and negative whole numbers, with 0 thrown in as well.
If k = 5 for instance, then 2k = 2*5 = 10 which is even.
Or if k = 27, then 2k = 2*27 = 54 which is also even.
We can show that 0 is even since,
2k = 0
k = 0/2
k = 0
So 2k = 2*0 = 0 is an even number.
Further Reading
https://mathworld.wolfram.com/EvenNumber.html
Answer by math_helper(2461)  (Show Source):
You can put this solution on YOUR website! An even number is a number which when divided by 2, leaves no remainder.
0 / 2 = 0 (no remainder, so zero is even since it passes the zero remainder test)
On a related note about zero (0): zero is neither negative nor positive. So when a problem says something like 'x is a positive number' you are dealing with a number that is strictly greater than zero. When the author wishes to include zero, you might see wording such as 'x is a nonnegative number...'.
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