# Natural numbers, infinity

In the crowd N of the natural numbers, every number n has an (immediate) successor n + 1. If you start counting at 1, you never come to an end, there are infinitely many natural numbers - https://domyhomework.club . They also say: the amount N of natural numbers is infinite.

In the crowd N of the natural numbers, every number n has an (immediate) successor n + 1:

The successor of 9 is 10, that of 1,000,000 is 1,000,001, that of 1,000,000,000,000,000 (one quadrillion) is 1,000,000,000,000,001 (one quadrillion and one).

It is therefore clear that there is no such thing as a greatest natural number.

Suppose someone claims to have discovered the greatest natural number - https://domyhomework.club/algebra-homework/ , take the successor of that number and have an even larger one. So the claim was wrong.

If you start counting at 1, you never come to an end, there are an infinite number of natural numbers. They also say - do my excel homework for me : the amount N of natural numbers is infinite.

A nice example of this is the following:

• Imagine a cosmic hotel with an infinite number of single rooms.
• The hotel is full.
• Now another guest comes. Can he still be accommodated in the fully occupied hotel?
• Yes. Since there are an infinite number of rooms, each guest only moves one room further and the first one becomes free.
• Of course, 10 guests can also be accommodated according to the same principle.
• An infinite number of guests can still find space here, you just have to repeat the procedure described above an infinite number of times.

The example shows that one has to be very careful with the term “infinite” in mathematics. Infinite is by no means to be understood as a number, but as a process of always-and-so-on-counting or thinking or crossing all limits. Infinite is therefore not synonymous with "incredibly large".

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