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↳ To Infinity and Beyond. Introduction

↳ Review of Set Theory

↳ Functions

↳ Countability

↳ Cardinality

↳ Hilbert's Grand Hotel

$ y = f(x) = x^4, f:\mathbb{R}\rightarrow\mathbb{R} $ Fig 2: $ f $ is not onto since there is no value on the $ x $-axis that can produce a negative real number on the $ y $-axis

References

• R. G. Bartle, D. R. Sherbert, "Preliminaries" in "An Introduction to Real Analysis", Third Edition, John Wiley and Sons Inc. 2000 ch. 1, sect. 1.1, pp 18.

• R. Kenney. MA 301. "An Introduction to Proof through Real Analysis", Lecture Notes. Faculty of the Department of Mathematics, Purdue University, Spring 2012

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