Esther Rantzen Esther Rantzen Dame Esther Louise Rantzen (born 22 June 1940) is an English journalist and television presenter, who presented the BBC television series "That's Life!" for 21 years, from 1973 until 1994. She works with various charitable causes, and founded the charities ChildLine, promoting child protection, which she set up in 1986, and The Silver Line, designed to combat loneliness, which she set up in 2012. Rantzen was born in Berkhamsted, Hertfordshire, England, to Katherine Flora Rantzen ("née" Leverson, 1911–2005) and Henry Barnato Rantzen (1902–1992). She has one younger sister, Priscilla N. Taylor. She attended Buckley Country Day School in
Well-founded relation R x". As an example, consider the well-founded relation (N, "S"), where N is the set of all natural numbers, and "S" is the graph of the successor function "x" → "x" + 1. Then induction on "S" is the usual mathematical induction, and recursion on "S" gives primitive recursion. If we consider the order relation (N, <), we obtain complete induction, and course-of-values recursion. The statement that (N, <) is well-founded is also known as the well-ordering principle. There are other interesting special cases of well-founded induction. When the well-founded relation is the usual ordering on the class of