Subset & deterministic noise

[apinde]

Related to Q1 in HW6 I used the following reasoning to say that there is no trend. Whats the falacy?

Construct the hypothesis set H as the union of two hypothesis sets H1 and H2
Let H1 have higher deterministic noise and H2 have lower
H will have deterministic noise between H1 and H2
Now let H' be the set H1. Clearly H' is a subset of H ans H' has higher deterministic noise than H
Similarly H' can be H2, and then H' has lower deterministic noise than H

Therefore there is no trend