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Similarly consider the math example of 3x7=21 and 1x21=21. It is certainly true that "3x7" and "1x21" pick out the same number and as a result, would not say that no information was gained by saying 3x7=1x21. We would not say this because we have learned that the expression "3x7" picks out the same number as the expression "1x21". [11]
It is often argued that open-ended questions (i.e. questions that elicit more than a yes/no answers) are preferable because they open up discussion and enquiry. Peter Worley argues that this is a false assumption. This is based on Worley's central arguments that there are two different kinds of open and closed questions: grammatical and conceptual.
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements.For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of Q is guaranteed by the truth of P.
This allows using them in any area of mathematics, without having to recall their definition. For example, if one encounters R {\displaystyle \mathbb {R} } in combinatorics , one should immediately know that this denotes the real numbers , although combinatorics does not study the real numbers (but it uses them for many proofs).
A function (which in mathematics is generally defined as mapping the elements of one set A to elements of another B) is called "A onto B" (instead of "A to B" or "A into B") only if it is surjective; it may even be said that "f is onto" (i. e. surjective). Not translatable (without circumlocutions) to some languages other than English. proper
The Principles and Standards for School Mathematics was developed by the NCTM. The NCTM's stated intent was to improve mathematics education. The contents were based on surveys of existing curriculum materials, curricula and policies from many countries, educational research publications, and government agencies such as the U.S. National Science Foundation. [3]
The use of many symbols is the basis of mathematical notation. They play a similar role as words in natural languages. They may play different roles in mathematical notation similarly as verbs, adjective and nouns play different roles in a sentence.
Although learning mathematics involves memorization of the sort of factual knowledge that Wikipedia provides, memorization is not enough to master the field. To become a mathematician, you must acquire the skills of creating proofs and doing calculations for yourself, to internalize the material; therefore, you must go beyond the outline a ...