The number 9 can not be factored in either 2's or 5's and it is not a prime number, it does however remain in the leftover series when calculating 100! and therefor your statement "-reduce all the numbers down to there prime numbers" is incorrect. Also problematic is factorizing a number like 10 to 5's; the result is 2*5 and 2 is most definately not a prime number either.

2*5 = 10 where neither 2 or 5 is a factor of 10. This is a direct counter example to your statement :"only multiplying by 10 or a factor of 10 will produce a trailing zero". The problem here is your use of the word "only"; if you had left that one out then the statement would have been truthful.


Again, like others, you have discribed a method of calculating the number of trailing zero's without proving that this method is actually producing the correct number of trailing zero's. As such you have ONLY proven the minimal amount of trailing zero's to be 24.

This is a small but very important difference in mathematics.

An example; I can show that 20 can be divided by 2 but this doesn't show that it can ONLY be devided by 2.

Interesting stuff right ? It actually factors in with alot of discussions of boat design we have on these forums. There too people "proof" stuff using simple but not "logically thorough" means, making their believes sometimes unfouded or even wrong.

One example of course being that shorter hulls are always slower and as such the F16's can never be as fast as F18's. They could "proof" this by showing that the shorter (and lighter) P16 is significantly slower then the Prindle 18 while the general layout of both designs is almost identical. This statement is in itself truthful but its extrapolation to the conclusion that therefor the smaller (and lighter) F16's must be significant slower then the very similarly designed F18's is simply wrong.

Or Bill Roberts favourite gem ; That where monohull top speeds are determined by Max Speed = 1.54 *sqrt(hull length), multihull top speeds are determined by Max Speed = 4.5 * sqrt(hull length)

You can proof the existance and validity of the first relation but not of the second even though one can show that both produce relative accurate max speeds for a range of boats (but not for the whole range of possible designs).

Showing that some results/statements are correct does not equate to proving that only they are correct or that they are always correct.

Interestingly enough the reverse is however true. A single counter example is enough to completely devalidate any given statement and as such equates as being a fully enclosed (counter) proof.

Wouter