Exploring the Philosophy and Mathematics of Real Numbers
By
EthanHeilman
Sesame, salt, and substance. A flagship bake.
Summary
The article explores the philosophical and mathematical concept of real numbers, highlighting the incompleteness of rational numbers and the necessity of forming the real number line to fill these gaps. It is an excerpt from a book on the philosophy of mathematics, providing an introduction to the subject grounded in mathematical inquiry.
Key quotes
· 3 pulledThe classical discovery of irrational numbers reveals gaps in the rational number line: the place where √2 would be, if it were rational, is a hole in the rational line.
Thus, the rational numbers are seen to be incomplete. One seeks to complete them, to fill these holes, forming the real number line ℝ.
The real real numbers—what are they? Must we answer?
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