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Help on displaying equations
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Let D be updated by:

where *d* is bounded by , ,
and the initial value of
.
Then:

**Proof:**
The highest D can be is if it is always updated with :

so . Similarly .

**
I should note this only works if
α
is between 0 and 1.
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**Proof:**
In the discrete case, Q is updated by:

so by Theorem B.1:

This can also be viewed in terms of temporal discounting:

Similarly:

For example, if , then . And (assuming ) as , .

Note that since , it follows that .

**Proof:**
In the discrete case, W is updated by:

so by Theorem B.1:

by Theorem B.2.

Similarly:

Note that since , it follows that .

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