A thought just struck me today after watching a lecture on the construction of the rational numbers. What is the definition of 'greater than (>)' and 'less than (<)' in the real number system. The only way I can think to describe it is to make some reference to the Euclidean distance between the number and zero and see which distance is greater or smaller but of course that is just using the term in the definition itself. I also thought about the number of steps it takes to construct the number from ZFC set theory. Again though, you have to have some concept of greater than or less than to determine which took more steps.(adsbygoogle = window.adsbygoogle || []).push({});

Any help would be appreciated

Thanks

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# What is the definition of greater than or less than in terms of real numbers?

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