WHAT IS A PROOF? This paper reports on the diversity of meanings attached to the words "proof" and "proving" by upper elementary school students and makes connections with similar usages by mathematicians and mathematics educators. Five dimensions of mea......
In mathematics, a statement is a sentence that describes mathematical numbers and variables, operations on those numbers and variables, and how those numbers and variables are related. Every statement in mathematics has a truth value of being true or false. ...
A logically accurate argument that establishes the truth of a particular assertion is known as a proof. The logical arguments convince the reader about the truth of a given statement. In a proof, there is an answer for every why. Proofs are useful in mathematics, computer science, and in ma...
But once the correct hypothesis is formulated, the principle of mathematical induction is often sufficient to provide the proof. (查看原文) [已注销] 2013-05-19 15:53:04 —— 引自第15页 Goldbach (1690-1764) has no significance in the history of mathematics except for this problem, which...
This means that the foundation of mathematics is the study of some logical and philosophical notions. We elaborate in simple terms that the deductive system involves four things: (1) A set of primitive undefined terms; (2) Definitions evolved from the undefined terms; (3) Axioms or postulates...
A theory that proved impractical in practice. A schedule that proved to be too demanding. Demonstrate To point out; to show; to exhibit; to make evident. Prove (transitive) To demonstrate that something is true or viable; to give proof for. I will prove that my method is more effective ...
19 December, 2024 in expository, math.MG | Tags: cosmic distance ladder, quaternions, spherical trigonometry | by Terence Tao | 21 comments Hamilton’s quaternion number system is a non-commutative extension of the complex numbers, consisting of numbers of the form where are real numbers, and...
It is now tempting to try to set up an approximately scale-invariant blowup solution. It seems that the first step in this is to construct a “soliton” type localized steady state solution, that is a solution , to the equation that decays in the variable; one can then hope to do a...
Mathematics Alive The Role of the Untrue in Mathematics Desperately Seeking Mathematical Proof An Enduring Error What Is Experimental Mathematics What Is Information-Based Complexity What Is Financial Mathematics If Mathematics Is a Language, How Do You Swear in It Mathematicians and the Pra...
Proof: We may assume is non-empty, as the claim is trivial otherwise. For any , define the quantity and let be a subset of that maximizes . Since and when , we see that . If the are distinct and , then we also have when , thus in this case we have . Let be the set (3...