What Is Hilbert’s Hotel?

What Is Hilbert's Hotel?

In mathematics, there are some really interesting thought experiments that help illustrate important concepts. One of my favorites is called Hilbert’s Hotel. It’s a thought experiment that was developed by German mathematician David Hilbert in 1924 to illustrate the concept of infinity. Here’s how it works.

There’s Always Room For One More!

Imagine that you are the manager of a hotel with an infinite number of rooms. One day, a woman comes to you and asks if you have any vacancies. You tell her that you do, and she checks in to Room 1. Later that day, another woman comes to you and asks if you have any vacancies. You tell her that you do, and she checks in to Room 2. This process continues throughout the day, with each new guest checking into the next available room.

Now, imagine that at 11 PM a man comes to you and asks if you have any vacancies. You tell him that you do, but all of the rooms are full. The man says not to worry, he’ll just take Room 1. So, you move the woman who is currently in Room 1 into Room 2, the woman in Room 2 into Room 3, and so on. This process continues until everyone has been moved up one room and the man can check into Room 1.

What’s interesting about this thought experiment is that it illustrates the fact that even though the hotel is full, there are still an infinite number of rooms available. That’s because infinity is not a number; it’s an idea. And as such, it’s something that we can only wrap our minds around by using our imaginations.

How Can God Be Infinite?


While Hilbert’s Hotel may seem like a simple thought experiment, it actually illustrates a very important concept: the infinity of God. Just as there are an infinite number of rooms in Hilbert’s Hotel, so too is there an infinite number of things that God knows (omniscience), an infinite number of places He can be (omnipresence), and an infinite number of things He can do (omnipotence). The infinity of God is one of His most amazing attributes!

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