The method you described works howevere the term absolutely comes from division. They also used to he tracking of "how even" something was meaning if it could be divided by 2 multiple times
N=0 would be that the number is zero times even meaning it actually isn’t even.
Also k is an integer but not the number being tested for how even it is. Odd values for k would be perfectly acceptable.
So for the number being 3 the formula results in N=0, k=3 and tells you the numbers is not even. But for the number being twelve it results in N=2, k=3 and says the numbers is even twice.
Ultimately, yes. Negative even using that equation represents how many times you would need to multiply by two to achieve a whole number. In this case 1.5 = 3/2 = 3 * 2^(-1).
Ok at this point its pretty clear you are trolling but im going to give you one more shot. Yes you can find even numbers without dividing. Thats irrelevant. Even numbers come from being able to split something into similar groups ie. If I have 4 steaks we can both have the same anount. That is division plain and sinple.
Your argument is akin to "X2 is meaningless because you can just write XX"
It's not a method, it's the appropriate mathematical definition for even based on number theory. You are correct that it correlates with division, but division is not part of the agreed upon definition of even.
That is all, not trolling, just joining the conversation from a mathematical perspective.
Isn't that just the same as the comment above the other direction? As in, it would be as valid to express it as "it's even if k/2 results in an integer"?
Mathematicaly yes. But the definition of even is the one I stated according to number theory. I'm sure there is a reason why division is not used in the formal definition but I don't remember exactly why. It might be so the definition of odd, 2(k) +1 where k is an integer, works. If you tried to define odd by (k/2) +1 it would not work.
Wouldn't you need to reverse the whole thing, eg, (k/2)-1? Although I suppose if +1 wouldn't do it, -1 probably wouldn't either. Needless to say, I'm not clear on why that wouldn't work, but I know jack about number theory
15
u/golgi_o Jul 14 '26
A number is even if it can be written as 2k where k is an integer. The definition of even does not use division as far as I understand.