Sets

Maths · Class 11

Simulation · Maths · Class 11

Build an interval

"Build an interval" is a free, interactive Class 11 Maths simulation for JEE, built on the lesson "Intervals as subsets of R" in Sets. Drag an orange dot to move that end. Tap a dot, or use the chips, to include the end (filled dot, square bracket) or leave it out (hollow dot, round bracket). (a, b), [a, b], [a, b) and (a, b] all have length b − a; they differ only at the two end points. An end at ∞ always takes a round bracket, because ∞ is not a real number that could be included. JEE Main asked 3 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).

From the lesson Intervals as subsets of R in Sets. Change the values and watch what happens.

Build an intervalMaths · Class 11

In JEE Main

42 shifts analysed

3 questions from Sets across the 42 JEE Main shifts Lumi has analysed (2017–2026).

The idea behind it

NCERT §1.6.1, §1.6.2

  • The number sets nest: N ⊂ Z ⊂ Q ⊂ R, where Q = {x : x = p/q, p, q ∈ Z, q ≠ 0}. The irrational numbers T = {x : x ∈ R and x ∉ Q} include √2, √5 and π; T ⊂ R and N ⊄ T.
  • For real a < b, the open interval (a, b) = {x : a < x < b} leaves out both end points, and the closed interval [a, b] = {x : a ≤ x ≤ b} keeps both.
  • The half-open intervals are [a, b) = {x : a ≤ x < b}, which keeps a and drops b, and (a, b] = {x : a < x ≤ b}, which drops a and keeps b.
  • Each of (a, b), [a, b], [a, b) and (a, b] has length b − a, and each contains infinitely many real numbers.
  • [0, ∞) is the set of non-negative reals, (−∞, 0) the set of negative reals and (−∞, ∞) the whole of R. The side at ∞ always takes a round bracket, because ∞ is not a real number that could be included.
  • Translating is routine: {x : x ∈ R, −2 < x ≤ 4} is the interval (−2, 4], and [1, 6) in set-builder form is {x : 1 ≤ x < 6}. On a number line an included end point is drawn as a filled dot and an excluded one as a hollow dot.

Questions

3 answers

What does the "Build an interval" simulation show?
Drag an orange dot to move that end. Tap a dot, or use the chips, to include the end (filled dot, square bracket) or leave it out (hollow dot, round bracket).
Does JEE Main ask questions from Sets?
Yes. JEE Main asked 3 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
Is this simulation free?
Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Intervals as subsets of R" in Sets (Class 11 Maths).

Embed this simulation

Free, with a link back

Teaching this idea? Put the simulation on your own page or LMS with this code.