#!/usr/bin/env python
# coding: utf-8

# # Chapter 5: Numbers & Bits (TL;DR)

# There exist three numeric types in core Python:
# - `int`: a near-perfect model for whole numbers (i.e., $\mathbb{Z}$); inherently precise
# - `float`: the "gold" standard to approximate real numbers (i.e., $\mathbb{R}$); inherently imprecise
# - `complex`: layer on top of the `float` type to approximate complex numbers (i.e., $\mathbb{C}$); inherently imprecise
# 
# Furthermore, the [standard library <img height="12" style="display: inline-block" src="../static/link/to_py.png">](https://docs.python.org/3/library/index.html) provides two more types that can be used as substitutes for the `float` type:
# - `Decimal`: similar to `float` but allows customizing the precision; still inherently imprecise
# - `Fraction`: a near-perfect model for rational numbers (i.e., $\mathbb{Q}$); built on top of the `int` type and therefore inherently precise
# 
# The *important* takeaways for the data science practitioner are:
# 
# 1. **Do not mix** precise and imprecise data types, and
# 2. actively expect `nan` results when working with `float` numbers as there are no **loud failures**.
# 
# The **numerical tower** is Python's way of implementing various **abstract** ideas of what numbers are in mathematics.