MEI

Real Numbers Lab

Mathematics for Engineers I · Module 62765 · Chapter 2

Commit to a prediction, rate your confidence, then reveal the mechanism. Finish an experiment’s four challenges to open its controls and try new values.

How the lab works

  1. Predict. Choose an answer before the stage changes.
  2. Rate your confidence. A sure but wrong answer marks an idea to revisit first.
  3. Reveal. Watch the rule play out and follow its link back to the guide.
  4. Explore. Finish all four challenges to open that experiment’s controls.

2.1 Number systems: binary place value

Each bit marks a power of two. Read the places from right to left, then add the marked values to recover the integer.

After the challenges, choose a numeral below, or type your own bits.

Choose a binary numeral
Or try your own

2.2 Suprema: rationals around √2

Rational lower and upper bounds can squeeze toward √2. The real numbers contain the least upper bound even though this particular set contains no maximum.

After the challenges, change the decimal precision below.

Set the decimal precision

2.3 Absolute value: distance on the line

The inequality |x−a|≤r describes all points at distance at most r from a. The center shifts the interval; the radius sets its width.

After the challenges, set the centre and radius below, or type your own.

Choose a center and radius
Or try your own

2.4 Binomial coefficients: Pascal’s rows

Each interior coefficient is the sum of the two above it. Row n supplies the coefficients for (a+b)n, while the term exponents run in opposite directions.

After the challenges, choose a row, or type any n up to 12.

Choose a Pascal row
Or try your own

2.5 Induction: start and advance

An induction proof establishes a starting case, then shows that any allowed case passes the statement to the next one. The chain cannot move until its first link is true.

After challenges, check the sum formula at a chosen n.

Choose an induction index

Your results

Scores are saved in this browser. “Sure, but wrong” highlights confident mistakes to revisit in the guide.

Personal interactive lab based on Mathematics for Engineers I lecture notes, Chapter 2 “Real Numbers” (printed pages 11–22), by Rhoslyn Coles and Cornelia Schneider. Not an official FAU publication; check course details against the current notes. Made by Thanate Amornjiraporn (Focus).