 Weierstrass was concerned to purge the foundations of analysis of all traces of the intuition of continuous motion—in a word, to replace the variable by the static. For Weierstrass a variable \(x\) was simply a symbol designating an arbitrary member of a given set of numbers, and a continuous variable one whose corresponding set \(S\) has the property that any interval around any member \(x\) of \(S\) contains members of \(S\) other than \(x\). Weierstrass also formulated the familiar \((\varepsilon , \delta)\) definition of continuous  function:[29]  a function \(f(x)\) is continuous at \(a\) if for any \(\varepsilon \gt 0\) there is a \(\delta \gt 0\) such that \(\lvert f(x) - f(a)\rvert \lt \varepsilon\) for all \(x\) such that \(\lvert x - a\rvert \lt  \delta\).[30]