Algebra Logic Flashcards
(11 cards)
What is a real number?
A real number is any value that can represent a distance along a continuous line, including all the numbers on the number line. This set includes:
Rational numbers: Numbers that can be expressed as the ratio of two integers (e.g., 1/2, -3, 4).
Irrational numbers: Numbers that cannot be written as a simple fraction, and have non-repeating, non-terminating decimal expansions (e.g., √2, π).
Real numbers include:
All positive and negative integers (…, -3, -2, -1, 0, 1, 2, 3, …)
All fractions and decimals (e.g., 0.75, -2.5)
All irrational numbers
In summary:
A real number is any number that can be found on the number line, encompassing both rational and irrational numbers. The set of real numbers is usually denoted by the symbol ℝ.
What symbol is commonly used to denote ‘such that’ in mathematical notation?
The vertical bar ‘|’ or a colon ‘:’
True or False: The symbol ‘∈’ represents ‘is an element of’.
True
Fill in the blank: The symbol ‘∀’ is used to represent ______.
for all
What does the symbol ‘∃’ signify in mathematics?
There exists
Multiple Choice: Which of the following symbols represents ‘not equal to’? A) = B) ≠ C) < D) >
B) ≠
What is the meaning of the symbol ‘ε’ (epsilon) in mathematics?
It often represents an arbitrarily small positive quantity.
True or False: The symbol ‘⊆’ means ‘is a subset of’.
True
What does the symbol ‘∑’ represent?
Summation
Fill in the blank: The symbol ‘→’ indicates ______.
implies
Multiple Choice: Which symbol is used for ‘approximately equal to’? A) = B) ≈ C) ≡ D) ∼
B) ≈
