/sci/ - Science & Math

>https://www.math.ucdavis.edu/~hunter/intro_analysis_pdf/intro_analysis.pdf
I was looking through some stuff. I found these nice chapters on real analysis. It says that
( R , +, · )

is a field. Therefore, R is not a field. Thus it demonstrated. Let it be known.

The contentious issue with R-hat not being a field is that it does not satisfy condition (f) related to the multiplicative inverse. Since we have added an exception for {0} and zero is still a real number, we may likewise add an exception for numbers in the neighborhood of infinity.

Detractors will say, "No, zero is the only exception because it is super special." I rebut that with, "The reason R-hat doesn't appear in the exceptions to (f) is because the author did not consider such numbers. If zero was an extra special super exception then the author would have written something like, 'Zero is the one and only exception to (f) and all other possible exceptions are ruled out by Theorem XXX.'"

In closing and without reference to my opinion about what the author would have done, take careful note that NOT all real numbers satisfy the field axioms. This is a fact. If you can add an exception for whomever came up with zero then you can add an exception for me. I'm not requesting a special exception. I am requesting the same exception afforded to the discoverer/inventor of the number/numeral zero.