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Full-Text Articles in Analysis
The Hyperreals: Do You Prefer Non-Standard Analysis Over Standard Analysis?, Chloe Munroe
The Hyperreals: Do You Prefer Non-Standard Analysis Over Standard Analysis?, Chloe Munroe
Mathematics Undergraduate Theses
The hyperreal number system *ℝ forms an ordered field that contains ℝ as a subfield as well as infinitely many large and small numbers. A number is defined to be infinitely large if |ω| > n for all n = 1, 2, 3, ... and infinitely small if |ε| < 1/n for all n = 1, 2, 3... This number system is built out of the real number system analogous to Cantor’s construcion of ℝ out of ℚ. The new entities in *ℝ and the relationship between the reals and hyperreals provides an appealing alternate approach to real (standard) analysis …