Tax basis is the counterpart of the GAAP concept of book value, and/but basis or adjusted basis

1. cannot be less than zero.
2. for any intangible asset is always the same as that assets GAAP book value.
3. can only increase, never decrease.
4. can only decrease, never increase.
5. is reduced, dollar for dollar, as associated cost recovery deductions are taken.
6. with respect to certain kinds or categories of assets may never (or rarely) change between the date of an assets acquisition and the date of its eventual sale or other disposition.

Since one or more of these six statements contradict one or more others, it is obvious that each cannot be true. Which statements are true, and why?