In the system of arithmetic we have adopted, zero is a number and infinity is not.
It is possible to extend our arithmetic in certain ways to include infinity as a number, but it is not trivial.
It is possible to extend our arithmetic in certain ways to include infinity as a number, but it is not trivial.
Comments
1) The BC/AD year was introduced 6 centuries after the biblical events of the New Testament, by a European monk. At the time, Europe had no concept of zero. That took another 600 years. Without the concept, there could be no “year zero”.
Likewise, the Ancient Greeks believed that all numbers could be expressed as the ratio of two whole numbers. But now, every school child discovers that PI “goes on forever” without repetition. Such numbers cannot be expressed as the ratio
And it gets worse. When we think about “square numbers” (numbers that are the result of multiplying numbers by themselves), we find that all positive numbers (and zero) can be the result of multiplying another number by itself (the “square root”).