Because a definition should hold true for all values.
If you define a set X as a set of natural numbers,and then i point out a x in X which is not a natural number then the definition is wrong,X is obviously not a set of natural numbers.
Or
The definition should specify something about the x of X in X - which it doesn't in this case so the definition is obviously wrong.
I'm not playing words games or anything i'm just saying what's obvious to me but apparently invisible to you...
(Also i refuse to blindly accept any definition just because it exists - some person,a person,made that definition,and people make mistakes,i've shown what mistake whoever that made that definition made.)
If you define a set X as a set of natural numbers,and then i point out a x in X which is not a natural number then the definition is wrong,X is obviously not a set of natural numbers.
Or
The definition should specify something about the x of X in X - which it doesn't in this case so the definition is obviously wrong.
I'm not playing words games or anything i'm just saying what's obvious to me but apparently invisible to you...
(Also i refuse to blindly accept any definition just because it exists - some person,a person,made that definition,and people make mistakes,i've shown what mistake whoever that made that definition made.)