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Questions and Answers
Which of the following best describes the use of 'and' in Mathematics language?
Which of the following best describes the use of 'and' in Mathematics language?
In Mathematics, 'is' may have a different meaning from its use in English when it is used to signify:
In Mathematics, 'is' may have a different meaning from its use in English when it is used to signify:
Which type of numbers are used for counting in Mathematics?
Which type of numbers are used for counting in Mathematics?
In Math language, which grouping symbols are commonly used?
In Math language, which grouping symbols are commonly used?
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What category does an equation fall under in the language of Mathematics?
What category does an equation fall under in the language of Mathematics?
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When translating from English to Math language, what do ordinal numbers signify?
When translating from English to Math language, what do ordinal numbers signify?
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What is the translation of 'Twice a number minus eight' into mathematical expression?
What is the translation of 'Twice a number minus eight' into mathematical expression?
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Which phrase translates to the expression 'x/7 = 2'?
Which phrase translates to the expression 'x/7 = 2'?
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If a set A = {2, 4, 6} and B = {a, b, c}, are they equivalent or equal sets?
If a set A = {2, 4, 6} and B = {a, b, c}, are they equivalent or equal sets?
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What is the product of a number and ten, if the result is eighty?
What is the product of a number and ten, if the result is eighty?
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Which expression represents 'A total of six and some number'?
Which expression represents 'A total of six and some number'?
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If 'Eight times a number is forty-eight', what is the mathematical expression for this statement?
If 'Eight times a number is forty-eight', what is the mathematical expression for this statement?
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What is the definition of a proposition?
What is the definition of a proposition?
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Which term describes a statement that conveys two or more ideas?
Which term describes a statement that conveys two or more ideas?
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In mathematical logic, what does a 'simple proposition' refer to?
In mathematical logic, what does a 'simple proposition' refer to?
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What does the vertical line test help determine in mathematics?
What does the vertical line test help determine in mathematics?
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Which symbol represents 'and' in mathematical language?
Which symbol represents 'and' in mathematical language?
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If P represents 'I study hard' and Q represents 'I get good grades', what does the compound proposition 'P and Q' signify?
If P represents 'I study hard' and Q represents 'I get good grades', what does the compound proposition 'P and Q' signify?
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Study Notes
Nature of Mathematics
- Language of mathematics is a system of conventional spoken, manual (signed), or written symbols that express human thought.
- Mathematics language has its own set of symbols, including English alphabet, numerals, Greek letters, grouping symbols, and special symbols.
Mathematics Language vs. English Language
- Difficulties arise from different meanings or uses of words in math and English, such as "and" equivalent to plus and "is" having different meanings.
- Numbers have different uses in math: cardinal (counting), ordinal (telling positions), and nominal (identifying).
Translation: English to Math Language
- Example translations: y = x, x = y, input-output functions, and function notation.
Functions
- A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range).
- Vertical Line Test: if a vertical line intersects the graph of a relation at more than one point, then the relation is not a function.
- Examples of functions and non-functions are provided.
Elementary Logic
- Logic serves as a set of rules governing the structure and presentation of mathematical proofs.
- A proposition is a statement that is either true or false, and can be expressed in symbols P, Q, R, or p, q, r.
Sets
- A set in mathematics is a collection of well-defined and distinct objects, considered as an object in its own right.
- Equivalent sets have the same cardinal number, while equal sets have identical elements.
KeyWords to Remember
- equals (=) is, are, was, were, will be, gives, yields, sold for, cost
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Description
Test your knowledge on the language of mathematics, the use of symbols in mathematics, sets, and elementary logic. Explore how mathematics uses a system of symbols to express concepts and ideas.
