1r BTL CCSS Notes 2026–27

Real numbers

Class notes, taught in Catalan. Published section by section as the course goes on.

The sets ℚ and 𝕀, how to tell them apart by their decimal expansion, and the diagram of the reals.

Sums and products of rationals and irrationals, and the problem of the two ants in love.

Open, closed and half-open intervals, set and real-line notation, and union and intersection.

Rational or irrational, the diagram of the number sets, and the first intervals and neighbourhoods.

The property tables for powers and radicals, and the sign and index traps.

Getting the roots out of the denominator: a square root, an $n$-th root and a binomial, with the conjugate.

Eight fractions to rationalise, with the solution to each part folded away.

What a logarithm is, base, argument and result, examples and the types: general, common and natural.

Radical and power, taking factors out, common index and operations with radicals, with each solution folded away.

Basic properties, product, quotient and power, change of base and an exponential equation.

Approximating logarithms with $\log 2 \approx 0.301$, writing a single logarithm and finding $x$, with each solution folded away.

The Richter scale, decibels and the log scale of stock charts, with interactive charts.