Pythagoras

So we all know that to find the length of a hypotenuse you use the formula A squared + B squared = C squared.  What happens, however, if A and B = 1 ?  Did Pythagoras note this problem?  Is 2 the only number with an infinite decimal for a square root?  How do you find the length of the hypotenuse in this situation?  

From Wikipedia:

<Wikipedia>
For any two related concepts, A and B; A is considered a generalization of concept B if and only if:

    * every instance of concept B is also an instance of concept A; and
    * there are instances of concept A which are not instances of concept B.

</Wikipedia>


Let A be the statement "If N is a positive integer and sqrt(N) is not an integer, then N is irrational" and B be the statement "If N is a positive integer having value 3, 5, 6, or 7, then sqrt(N) is odd".

Then every statement of B is also an instance of concept A (since 3,5,6, and 7 are positive integers) , and there exist instances of concept A (i.e., positive integers whose square roots are not integers) that are not instances of concept B. Then statement A is a generalization of concept B.


If anyone sees any serious flaws with the above reasoning, please point them out.


What >>3 etc. did was "specify" (i.e. define) the general rule for determining whether the square root of a number is irrational. Then the rest of the thread used the logical meaning of "specify" (one case of a general statement) whereas >>3 etc. use the meaning "to define".


Thread over?