2 - Jesse Hyttinen

Hi and welcome to the Matladpi blog!

Have you ever noticed how

3! = 3*2*1 = 3+2+1?

Or how

2^2 = 2*2 = 2+2?

Or how

2^0 + 2^-1 + 2^-2 + 2^-3 +... = 2?

Or how in every one of these examples, there is at least one number two?

2 has unique properties as a number. For example, it is the only even prime number, as every even number can be expressed as a multiple of 2. For a brain teaser, especially if you do not know the power of compounding interest, try the following:

Which is larger, 1000 or 2^10?

You may be surprised, but actually 2^10 is the larger one! I can demonstrate this:

Let us begin at the exponent of 0, and increase this by one in each step. The actual number will be displayed next to this number. In each step for the 2^n column, we double the previous number to gain the next one.

n 2^n

0 1

1 2

2 4

3 8

4 16

5 32

6 64

7 128

8 256

9 512

10 1024

As you can see, 2^10 = 1024 > 1000.

In the same manner, 2^20 > 1 000 000 and

2^30 > 1 000 000 000. If you actually think of it, we have a result

2^10 > 10^3

(2^10)^n > (10^3)^n

2^(10*n) > 10^(3*n)

2^(10n) > 10^(3n)

for every nonzero integer.

I am Jesse Sakari Hyttinen and I will see you in the next post!