Changes

This approach is analogous to proof by induction except infinite descent goes in the backwards, or downwards, direction until a contradiction occurs, thereby proving the falsehood of the hypothesis.  The approach can be summed up as this:

This approach is analogous to proof by induction except infinite descent goes in the backwards, or downwards, direction until a contradiction occurs, thereby proving the falsehood of the hypothesis.  The approach can be summed up as this:

:Assume that a solution to an equation exists among positive integers.  Then show that the existence of that solution implies the existence of another solution with smaller natural positive integers.  Then show that yet another solution among positive integers must exist, and so on ad infinitum.  But descent ad infinitum is impossible among positive integers, and hence a contradiction occurs.  Therefore no solution can exist among positive integers.

:Assume that a solution to an equation exists among positive integers.  Then show that the existence of that solution implies the existence of another solution with smaller natural positive integers.  Then show that yet another solution among positive integers must exist, and so on ''ad infinitum''.  But descent ''ad infinitum'' is impossible among positive integers, and hence a contradiction occurs.  Therefore no solution can exist among positive integers.

 

A better name for "infinite descent" as used in mathematics could be "descent until contradiction," because the point of infinite descent is to show that if a hypothesis were true, then an impossible infinite consent would be possible.  The contradiction disproves the hypothesis.

== Infinite descent and the [[Bible]] ==

== Infinite descent and the [[Bible]] ==