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 sets are well-founded. A relation "R" is converse well-founded, upwards well-founded or Noetherian on "X", if the converse relation "R" is well-founded on "X". In this case "R" is also said to satisfy the ascending chain condition. In the context of rewriting systems, a Noetherian relation is also called terminating. An important reason that well-founded relations are interesting is because a version of transfinite induction can be used on them: if ("X", "R") is a well-founded relation, "P"("x") is some property of elements of "X", and we want to show that it suffices to show that: That is, Well-founded induction