Answer :
Let's talk about sets!
So the most basic set is natural numbers. (aka counting numbers)
These are: 1, 2, 3, 4, 5, 6, 7... (may or may not include 0, it doesn't matter)
Then we have our intergers.
These are: 0, 1, 2, 3, 4, 5...and all of their negative counterparts: -1, -2, -3, -4, -5...
Then we have numbers that can be displayed as fractions, known as rational #'s.
All intergers would be rational, just display them as over 1.
All fractions, (1/2) decimals, (0.5) and numbers with repeating decimals that follow a pattern (1/3, 1/7) are all included.
Lastly, there's real numbers. This is just rational and irrational numbers together. These would include π, 2π, and various other mathematical constants.
Here's how you represent these in mathematical notation:
x is an element of ⇒ x ∈
the natural numbers ⇒ ℕ (you'd read this as "x is an element of the natural numbers")
the intergers ⇒ ℤ
the rational numbers ⇒ ℚ (the Q stands for quotient)
the real numbers ⇒ℝ
Of course, there's also the negative interger (less than 0) and greater than or equal to -8 part.
You should know this already. The "mouth" eats the larger number.
> greater than
< less than
≥ greater than or equal to
≤ less than or equal to
When we put this all together, we need to first put it in braces to represent a set, (the set) have x and a vertical bar (of all x, such that) along with our statements about the numbers in the set. Finally we end up with
{ x | x ∈ ℤ, x < 0, x ≥ -8 }
(The numbers in this set would of course be -1, -2, -3, -4, -5, -6, -7, and -8.)
So the most basic set is natural numbers. (aka counting numbers)
These are: 1, 2, 3, 4, 5, 6, 7... (may or may not include 0, it doesn't matter)
Then we have our intergers.
These are: 0, 1, 2, 3, 4, 5...and all of their negative counterparts: -1, -2, -3, -4, -5...
Then we have numbers that can be displayed as fractions, known as rational #'s.
All intergers would be rational, just display them as over 1.
All fractions, (1/2) decimals, (0.5) and numbers with repeating decimals that follow a pattern (1/3, 1/7) are all included.
Lastly, there's real numbers. This is just rational and irrational numbers together. These would include π, 2π, and various other mathematical constants.
Here's how you represent these in mathematical notation:
x is an element of ⇒ x ∈
the natural numbers ⇒ ℕ (you'd read this as "x is an element of the natural numbers")
the intergers ⇒ ℤ
the rational numbers ⇒ ℚ (the Q stands for quotient)
the real numbers ⇒ℝ
Of course, there's also the negative interger (less than 0) and greater than or equal to -8 part.
You should know this already. The "mouth" eats the larger number.
> greater than
< less than
≥ greater than or equal to
≤ less than or equal to
When we put this all together, we need to first put it in braces to represent a set, (the set) have x and a vertical bar (of all x, such that) along with our statements about the numbers in the set. Finally we end up with
{ x | x ∈ ℤ, x < 0, x ≥ -8 }
(The numbers in this set would of course be -1, -2, -3, -4, -5, -6, -7, and -8.)
