Division by Zero - Can it be Done?

In summary, division by zero is a controversial topic in mathematics. While it is generally accepted that dividing by zero is undefined and leads to illogical answers, there have been attempts to create a new number system where division by zero is allowed. However, these systems are not considered to be true arithmetic and are not widely accepted. Some argue that in certain contexts, such as taking limits, dividing by zero can be useful. Ultimately, the laws of arithmetic prove that any system in which division by zero is allowed is not a field and leads to contradictions.
  • #36
What paradox? Every 'paradox' is based upon making some false assumption and then getting a contradiction. This is no different. Your false assumption is that things ought to behave in some way when they don't.
 
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  • #37
Vernon said:
How would this fit into the Cantorian hierarchy of infinities?

The infinity sign that appears in such things like this, singularities, is nothing to do with cardinals.
 
  • #38
matt grime said:
What paradox? Every 'paradox' is based upon making some false assumption and then getting a contradiction.
So the term "false paradox" is a pleonasm?
 
  • #39
I should have said 'every mathematical paradox'.
 

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