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Domain & Range Viewer

Interval notation · bracket types · union · intersection · visual number lines

Interval Notation Builder

Domain (x-axis)

ℝ:

only:

Range (y-axis)

ℝ:

only:

Codomain (y-axis)

ℝ:

only:

Number Line Viewer

🖱 scroll to zoom↕ drag to pan∞ infinite range

📐 2D Coordinate Grid — Domain × Range

D∩Range D∩Codomain

Intersection:

Functions

sample pts:

quick add:

Domain

🖱 scroll · drag · pinch

Co domain

Number Sets Explorer

Explore how ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ. Perform Union ∪, Subtraction ∖, and Multiplication × on any two number sets and see what you get.

ℕ Natural (1,2,3…)

𝕎 Whole (0,1,2,3…)

ℤ Integers

ℚ Rational

ℝ Real

ℝ∖ℚ Irrational

ℚ∖ℤ Fractions

ℤ∖𝕎 Neg. Integers

{0} Zero

Nesting Diagram ℕ ⊂ 𝕎 ⊂ ℤ ⊂ ℚ ⊂ ℝ

ℕ = {1, 2, 3, …}  — counting numbers (no zero)
𝕎 = {0, 1, 2, 3, …}  — whole numbers (ℕ + zero)
ℤ = {…,−2,−1, 0, 1, 2,…}  — integers (𝕎 + negatives)
ℚ  — rationals (ℤ + fractions p/q)
ℝ  — reals (ℚ + irrationals like √2, π)

Set Operation Calculator

Set A

Operation

Set B

Select sets and an operation above…

Closure Reference — Is the set closed under this operation?

      ✓ closed — the result always stays in that set  | 
      ✗ not closed — result may fall outside  | 
      ~ partial — depends on inputs
    

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