Re:Six Math Essentials by Terence Tao
by adrian_b on Wednesday November 11, 2026 @07:46AM
(#50452752)
Set theory and logic stay below numbers, but they do not belong to quantitative thinking.
By definition, quantities, either discrete or continuous, as already classified by Aristotle, are the properties that can be expressed by numeric values, as a result of counting for discrete quantities, or as a result of measuring for continuous quantities.
Properties that are not quantities, but which can be compared, to determine which is greater or less, or if they are equal, are qualities.
The simplest numbers, i.e. cardinal numbers a.k.a. natural numbers, are equivalence classes of sets, so indeed the theory of numbers is built upon that of sets (a.k.a. multitudes in older language), but this does not contradict in any way the title from the book, because quantitative thinking refers to only a part of mathematics, not to all of ite.
By definition, quantities, either discrete or continuous, as already classified by Aristotle, are the properties that can be expressed by numeric values, as a result of counting for discrete quantities, or as a result of measuring for continuous quantities.
Properties that are not quantities, but which can be compared, to determine which is greater or less, or if they are equal, are qualities.
The simplest numbers, i.e. cardinal numbers a.k.a. natural numbers, are equivalence classes of sets, so indeed the theory of numbers is built upon that of sets (a.k.a. multitudes in older language), but this does not contradict in any way the title from the book, because quantitative thinking refers to only a part of mathematics, not to all of ite.