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LUB4: Fractions Immediately Surrounding Any Real Number

*"*For any [real number] *x* and positive integer *N*, there is an integer *n* such that .*"* *(see ita-2-3-14-pg26)*

*"*To show this we merely have to apply LUB3 to the number *Nx*, getting an integer *n* such that .*"* *(see ita-2-3-14-pg26)*

Note that we can't use O3 to get from Rosenlicht's intermediate result, , to the final desired result (by multiplying both sides of the inequalities by 1/N) because we are missing the greater than zero condition. Instead, please see my first reading of LUB4 here.

Converted by *Mathematica*
December 4, 2007