Well, "math" is just a system of symbols and rules for manipulating them. There are different sets of rules and symbols that define different "maths". The old greeks considered only whole numbers and quotas between such, later an improved system was developed that accepted irrational numbers, and again that system was later extended to include complex numbers and even hypercomplex numbers. All these systems are applicable to phenomena in our physical world. There is but one keyissue in creating any such symbolhandling system and that is that there should be no contradictions in it - it'should be sound.Our "normal math" does not allow such things as division by zero and infinities. I think that's a shame. And I think that the "normal math"-system can be yet extended/modified, without any contradictions, to allow division by zero and treat the resulting infinity as a number, the antipode of 0.
My question is if any mathematician have bothered to research and construct such a symbolhandling system.
Now, I am familiar with G. Cantors approach regarding infinitely (and bigger) large sets and the related topic of infinite ordinal number, but that's not the kind of system I'm looking for. I'm looking for a system that only talks about numbers, that is, the set of consideration is the set of all real numbers and the anti-0-number. And our usual operators such as multiplication, division, addition etc. should be included. For small numbers they should work as ususal but they should also be defined for numbers in the surroundings of the anti-0-number. For instance, there should be an answer to the question "what is (1/0 + pi)e" that is a number in our set of consideration.
Has any such arithmetic that allow division by zero ever been constructed?
*regards
Printer-friendly copy
Email this topic to a friend
