Do you mean physically going through your cash, dollar by dollar, and tallying it up? Or cent by cent? Without any help? All by hand and memory counting?
If it's cent by cent then 100000000 dollars is 100000000000 cents. The oldest person ever lived to be 122 yeas and 164 days old. That's 44694 days (roughly, haven't included the extra day that comes with gap years). But let's assume that you spend 1/4 of that asleep. So you have 33520.5 days of wakedness in which to count your cents. So that means you'd have to count 100000000000/33620.5 = 2083249.057 cents per day. Which is 124302.044 cents per hour, which is 2071.7 cents per minute, which is 34.53 cents per second. Clearly impossible.
If you're counting dollar by dollar, and you live to the age of the oldest man ever than it might just be possible assuming you eat and drink while you count. However if you assume that you only live to the average oldest age, then that's about 70-80, then it should work out impossible do do it dollar by dollar also.
Bit ridiculous though trying to prove a 'theorem' that isn't really a 'theorem', but in fact, a figure of speech.