In the previous two posts, we have discussed about the logical operators and, or, and not. Those two articles are preparation for this post. Consider the following inequalities. 1.) 2.) The first inequality can also be represented as or . Now, how do we find not ( or ). To easily understand the question, […]

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# Set Theory

## One to One Correspondence and Hilbert’s Grand Hotel

In the Understanding Hilbert’s Grand Hotel, we have discussed the brilliant schemes of a hotel manager in accommodating finite and infinite number of guests in a hotel with infinite number of rooms, where each room was occupied by one guest. In other words, the hotel was fully occupied. In this post, I will explain the mathematics […]

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## The Number of Points on Two Line Segments

We say that a set is countably infinite if we can pair the elements with set of counting numbers 1, 2, 3, and so on. Believe it or not, the number of positive integers and the number of integers (both negative and positive including 0) have the same number of elements. It is because we […]

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