
Many of the basic inequalities involving real numbers spring from one of the most fundamental facts about reals: the square of a real number is always non-negative. Some of the inequalities given are here also related to properties of the exponential and the logarithmic functions. The reader is encouraged to explore these connections.
1. The AM-GM inequality
2. The Cauchy-Schwarz inequality
3. The exponential function
4. The natural logarithm