問題一覧
1
Able to express complex thoughts with relative ease.
Powerful
2
The members of a set are usually called its ___, and the symbol ∈ is usually read “_______”
Elements, is an element of
3
A set of ordered pairs. An alternative definition of what it means for a relation ~, defined on a set A, to be an equivalence relation is that it has the following three properties.
Relations
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____, which means that x ~ x for every x in A.
Reflexive
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A ___ of symbols or words.
Vocabulary
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__ denotes the dependent variable.
y
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A ___ of people who use and understand these symbols.
Community
8
The set of all resulting values of y is called the ___ of the function.
Range
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A ___ of meanings that can be communicated with these symbols.
Range
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End of the alphabet.
Variables (Unknown)
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A ___ consisting of rules on the use of these symbols.
Grammar
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It is a collection of both symbols and their meaning shared by a global community of people who have an interest in the subject.
Mathematics
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It is a system of communication about objects like numbers, variables, sets, operations, functions, and equations.
Mathematics
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From I to n.
Positive Integers (Counting)
15
____, which means that if x and y are elements of A and x ~ y then it must also be the case the y ~ 𝑥.
Symmetric
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f(x) is called as a ___.
Function Value
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Able to say things briefly.
Concise
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It is a name given to a mathematical object of interest.
Expression
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Start of the alphabet.
Constants (Fixed Values)
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These have conventions.
Languages
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A collection of objects, and in mathematical discourse these objects are mathematical ones such as numbers, points in space or other sets.
Sets
22
__ denotes the independent variable.
x
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The mathematical analogue of a ‘sentence’ will be called a ___.
Sentence
24
Able to make very fine distinctions.
Precise
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____, meaning that if x, y and z are elements of A such that x ~ y and y ~ z, then it must be the caser that x ~ z.
Transitive
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The mathematical analogue of a “noun” will be called an ___.
Expression
27
The language of mathematics makes it easy to express the kinds of thoughts that mathematicians like to express. It is:
Precise, Concise, Powerful
28
It is a systematic means of communicating by the use of sounds or conventional symbols.
Language
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It is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
Bijection
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The set of all admissible values of x is called the ___ of the function.
Domain
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read as “f of x”
f(x)
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It is the code that humans use as a form of expressing themselves and communicating with others.
Language
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A function that takes pairs of elements of A and produces elements of A from them. It is a function with the set of all pairs (x, y) of elements of A as its domain (x) and with A as its range (y).
Binary Operations
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f(x) is due to Swiss Mathematician and Physicist _____ (1707 – 1783).
Leonhard Euler
35
It is a set of ordered pairs of number (x, y) in which no two distinct ordered pairs have the same first number.
Function
36
4 Basic Concepts
Sets, Functions, Relations, Binary Operations
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It may also be defined as system of words used in a particular discipline.
Language