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Questions and Answers
What is language?
What is language?
A systematic means of communicating ideas or feelings by the use of conventionalized signs, sounds, gestures, or marks having understood meanings.
According to Dr. Burns, what are the three characteristics of the language of mathematics?
According to Dr. Burns, what are the three characteristics of the language of mathematics?
Precise, concise, powerful.
Which of the following are types of mathematical symbols?
Which of the following are types of mathematical symbols?
What is a mathematical expression?
What is a mathematical expression?
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What is a mathematical sentence?
What is a mathematical sentence?
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An open sentence is a sentence that uses ______.
An open sentence is a sentence that uses ______.
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A closed sentence is known to be either ______ or ______.
A closed sentence is known to be either ______ or ______.
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Is the statement '10 is an odd number' a closed sentence and is it true or false?
Is the statement '10 is an odd number' a closed sentence and is it true or false?
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Is the statement '4 + 5x = 9' an open or closed sentence?
Is the statement '4 + 5x = 9' an open or closed sentence?
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Translate the phrase 'decreased by' into a mathematical operation.
Translate the phrase 'decreased by' into a mathematical operation.
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Which of the following represents multiplication in mathematical terms?
Which of the following represents multiplication in mathematical terms?
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Study Notes
Mathematics as a Language
- Language is a system for communicating using signs, sounds, or marks with understood meanings
- Mathematics can be considered a language
- According to Dr. Burns, mathematical language is precise, concise, and powerful
- Mathematical language allows mathematicians to express complex thoughts easily
Classifications of Symbols
- Numbers include real numbers (ℝ), rational numbers (ℚ), irrational numbers (ℚ’), integers (ℤ), and natural numbers (ℕ)
- Operation Symbols include addition (+), subtraction (-), multiplication (x or ), division ( or /), and exponentiation (𝑥 𝑛 )
- Relation Symbols include greater than or equal ( ), less than or equal (), equal ( ), not equal ( ), similar (), approximately equal (), and congruent ()
- Grouping Symbols include parentheses ( ), curly brackets or braces { }, or square brackets [ ]
- Variables are used for quantities that change and are often represented by letters
- Set Theory Symbols include subset ( ), union (), intersection (), element (), not element (), and empty set ( )
- Logic Symbols include implies (), equivalent (), and (), or (), for all (), there exists (), and therefore ()
- Statistical Symbols include sample mean (𝑥), population mean (), median ( 𝑥 ), population standard deviation (), summation ( ), and factorial (n!)
Mathematical Expression and Sentence
- A mathematical expression is a phrase that combines symbols that can represent numbers, variables, operations, and other punctuation, but does not represent a complete thought
- A mathematical sentence makes a statement about two expressions, using symbols or words like equals, greater than, or less than, and expresses a complete thought
- An open sentence contains variables and its truth value is unknown
- A closed sentence has a truth value that is either true or false
Translating phrases to mathematical expressions and sentences
- Addition: plus, combined with, increased by, added to, the sum of, more than, total
- Subtraction: minus, decreased by, fewer than, less than, subtracted from, take away
- Multiplication: times, twice (times 2), thrice (times 3), squared, cubed, the product of, multiplied by, of
- Division: divided by, the quotient of, half of, a third of, ratio, shared equally
- Equality: equals, is, the same as, yields, amount to
- Inequality: less than or equal ( ), greater than or equal ( ), at most, at least, not greater than, not less than
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Description
Explore the concept of mathematics as a powerful language in this quiz. Delve into the classifications of symbols used in mathematical expressions, including numbers, operation, relation, and grouping symbols. Test your understanding of how these elements communicate complex ideas in mathematics.
