問題一覧
1
The language of mathematics makes it easy to express the kinds of thoughts that mathematicians like to express. It is:
Precise, Concise, Powerful
2
Able to make very fine distinctions.
Precise
3
Able to say things briefly.
Concise
4
Able to express complex thoughts with relative ease.
Powerful
5
It is a systematic means of communicating by the use of sounds or conventional symbols.
Language
6
It is the code that humans use as a form of expressing themselves and communicating with others.
Language
7
It may also be defined as system of words used in a particular discipline.
Language
8
A ___ of symbols or words.
Vocabulary
9
A ___ consisting of rules on the use of these symbols.
Grammar
10
A ___ of people who use and understand these symbols.
Community
11
A ___ of meanings that can be communicated with these symbols.
Range
12
It is a system of communication about objects like numbers, variables, sets, operations, functions, and equations.
Mathematics
13
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
14
Start of the alphabet.
Constants (Fixed Values)
15
From I to n.
Positive Integers (Counting)
16
End of the alphabet.
Variables (Unknown)
17
The mathematical analogue of a “noun” will be called an ___.
Expression
18
It is a name given to a mathematical object of interest.
Expression
19
The mathematical analogue of a ‘sentence’ will be called a ___.
Sentence
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These have conventions.
Languages
21
4 Basic Concepts
Sets, Functions, Relations, Binary Operations
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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
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The members of a set are usually called its ___, and the symbol ∈ is usually read “_______”
Elements, is an element of
24
It is a set of ordered pairs of number (x, y) in which no two distinct ordered pairs have the same first number.
Function
25
The set of all admissible values of x is called the ___ of the function.
Domain
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The set of all resulting values of y is called the ___ of the function.
Range
27
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
28
__ denotes the independent variable.
x
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__ denotes the dependent variable.
y
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read as “f of x”
f(x)
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f(x) is called as a ___.
Function Value
32
f(x) is due to Swiss Mathematician and Physicist _____ (1707 – 1783).
Leonhard Euler
33
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
34
____, which means that x ~ x for every x in A.
Reflexive
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____, 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
36
____, 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
37
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