On Tuesday, April 29, 2014 2:50:51 AM UTC-4, muec...@rz.fh-augsburg.de wrote: > Couldn't just the seemingly so fruitful hypothesis of the infinite have straightly inserted contradictions into mathematics and have fundamentally distroyed the basic nature of this science which is so proud on its consistency? > > > > Find the resolution tomorrow in >
Whoever said it has obviously not tried to formalize number theory on a finite set of any size (one with a beginning and an end). You might be able to construct an add function, but, from my experience, simple properties like associativity and commutativity seem to be impossible to establish. Addition, multiplication and exponentiation must be closed on the natural numbers. Arbitrarily assigning a successor to the largest number, or inserting an element into your set of natural numbers to be the "overflow" number are nothing more than an inelegant kluge.