Ruang Bukti

Understanding Real Numbers

Tue, 26 May 2026 21:31:11 +0200

What Are Real Numbers?

Real numbers are often introduced as “all numbers on the number line”.

That is a useful picture, but it hides a deeper question:

What exactly is this number line made of?

From counting to measurement

Natural numbers appear when we count:

$$ 1,2,3,\ldots $$

Integers appear when we allow subtraction:

$$ \ldots,-2,-1,0,1,2,\ldots $$

Rational numbers appear when we allow division:

$$ \frac{p}{q}, \quad q \neq 0. $$

About

Tue, 26 May 2026 20:27:07 +0200

Welcome to Ruang Bukti

Ruang Bukti is a personal project about mathematics, radar, signal processing, and numerical simulation.

The motivation behind this project comes from my experience studying and working in applied mathematics and numerical simulation.

I felt that high-quality resources in Indonesian are still very limited, especially for finite element methods (FEM), a subject I spent several years studying during my Ph.D..

Most available FEM resources are written primarily for mechanical or civil engineering students, often with a very application-oriented perspective. While those approaches are valuable, I wanted to create a resource that approaches FEM from a more mathematical point of view — starting from analysis, functional analysis, variational formulations, and gradually moving toward implementation and simulation.

Welcome to Ruang Bukti

Tue, 26 May 2026 20:23:46 +0200

Welcome to Ruang Bukti

This is the beginning of my notes on mathematics, radar, and numerical simulation.