# 2.4Cardinality of Sets

## 2.4.1 Introduction

No one knows exactly when people first started counting, but a good guess might be when people started accumulating things. However, long before number systems were invented, two people might have determined whether they had the same number of goats and sheep as illustrated in Figure 2.20 by simply placing them in a one‐to‐one correspondence with each other.

Another person might have designated a stone for each goat, thus obtaining a one‐to‐one correspondence between the goats and a pile of stones. Today, we no longer use stones to enumerate things since we have symbolic stones in the form of 1, 2, …. To determine the number of goats, we simply “count,” 1, 2, … and envision the rocks R = {1, 2, 3, 4, 5} in our mind as illustrated in Figure 2.21.

Throughout the history of mathematics, the subject of infinity has been mostly taboo, more apt to be included in discussions ...

Get Advanced Mathematics now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.