Well, let's see . . . . .
3 + 5 = 8
5 + 15 = 20
7 + 19 = 26
31 + 27 = 58
49 + 11 = 60
It's looking bad for your proposed rule.
This can actually be proven.
Any odd number can be expressed as 2p + 1 where pis any integer.
Let a = 2p + 1 and b = 2q + 1 where p and q are any two integers. Then, by definition, a and b are both odd, so lets add them up.
We know that any two integers added together equals another integer, the question is whether or not that integer is even or odd.
Let m be the integer such that a + b = m.
Substituting, we get (2p + 1) + (2q + 1) = m or 2p + 2q + 2 = m.
Dividing by 2 we get p + q = m/2 - 1.
Since p and q are both integers, m/2 - 1 must also be an integer. Therefore, m must be an even number.
Substituting the expression for p into the expression for a from above we get:
a = 2(m/2 - 1 - q) + 1 = m - 2 - 2q + 1 = m - (2q + 1) = m - b.
Therefore, a + b = m where a and b were both defined to be odd and m was previously shown to be even.
Thus, an odd + an odd = an even.
Q.E.D.
An even number
Yes.
An even number.
1+1=2
Any odd number can be written as an even number plus one. Any even number plus any other even number makes an even number. Add one makes an odd number. So an odd number plus an even number is always an odd number. Algebraically, any odd number can be written as 2a+ 1 where a is a whole number. Any even number can be written as 2b, where b is a whole number. Add them together, the sum is 2(a + b) + 1, which is odd.
An odd number plus an even number will always be an odd number.
An even number
Yes.
Yes because 12+11 = 23 which is an odd number
An even number.
1+1=2
In normal arithmetic, never.
Any odd number can be written as an even number plus one. Any even number plus any other even number makes an even number. Add one makes an odd number. So an odd number plus an even number is always an odd number. Algebraically, any odd number can be written as 2a+ 1 where a is a whole number. Any even number can be written as 2b, where b is a whole number. Add them together, the sum is 2(a + b) + 1, which is odd.
It doesn't. An even number(for example 2) plus an odd number(for example 3) would give you an odd number for the answer. Comment: Im sorry but you are mistaken, 2 is an odd number 2/2 2/1 so 2+4=6 see?
It is an odd number.
... equals an even number
You'll get an odd number when adding two evens (which will be even) and an odd number.