Toolbox
A formula sheet plus reference tools for calculator, equation solver, units, elements, graphs and molecules.
Number Line & Number Sets
Pan and zoom a number line, highlight nine number sets, browse 500 integers either side
Drag the line to pan, scroll or use +/− to zoom, and click a number below to jump.
- 1Rule
It equals 0, the boundary between positive and negative.
- 2Rule
It is divisible by 2, so it is even.
- 3Conclusion
0 is less than 2, so it is neither prime nor composite.
Concept
A number line fixes an origin, a positive direction and a unit length: 0 sits at the origin, right is positive and left is negative. Every real number has exactly one place on it.
Natural numbers include 0 (0, 1, 2, 3…), positive integers do not. 1 is neither prime nor composite, and 2 is the only even prime.
Parity depends only on the remainder modulo 2: remainder 0 means even, remainder 1 means odd. Zero is even.
Going further
- Rational and irrational numbers
- Not every point on the line is rational. √2 cannot be written as a fraction and sits at about 1.4142; π ≈ 3.1416, e ≈ 2.7183, log₂10 ≈ 3.3219.
- Testing for primes
- To decide whether n is prime, divide by primes up to √n. If none divides evenly, n is prime — exactly what the step-by-step check on this page does.
- Density of the rationals
- Between any two different rationals there is another rational (take the average), so rational points are packed densely — yet gaps remain, and the irrationals fill them.
Common mistakes
- Odd, even, prime and composite only make sense for integers; 0.5 is not part of the discussion.
- Negative odd numbers exist (−3, for example); test the remainder of the absolute value.
- 1 is neither prime nor composite, and 2 is the only even prime.