00:02
In this question, we are given a function fee from the rational numbers to the group of integers under addition by the formula fee of x is equal to sealing x.
00:14
Basically, sealing means rounding up to an integer.
00:17
For example, if you have sealing 5 .9, sealing 5 .9 is equal to 6.
00:24
But also ceiling of 5 .1 is equal to 6.
00:30
So basically we're rounding our number or a rational number.
00:35
We're rounding it up.
00:37
Now let's, and we're asked whether fee is a homomorphism.
00:42
Now let's recall what a homomorphism is.
00:44
Homomorphism means for all x, y, in q, we want fee of x plus y to be equal to fee of x.
00:56
Plus fee of y.
01:01
In our case, this is not true and it's easy to find the counter example...