Random.org and randomness

Your calculator cannot produce random numbers.
Neither can your computer.
The lottery does not produce random numbers.
The human being, in particular, cannot produce random numbers.

All of these things are biased in some way. Human beings are the worst: if asked to think of a number between 1 and 10, most people will tend to say the number 7. Further, most people will tend to think of odd numbers, as they somehow think they are “more” random. Try it on your friends!

Computers and calculators use computer programs that suggest random numbers. However, these are not random in the slightest – they are just based on very complicated mathematical functions, and mimic random numbers well enough to be used in most real-world applications. These numbers are often said to be pseudorandom.

However, atmospheric radiation is completely random, and is used by random.org to produce truly random sequences. Try the following:

Roll 16 dice.

Generate truly strong passwords (8 letters/numbers long).

Pick lottery numbers (with which your chances of winning are 1 in 13,983,816).

Generate a number between 1 and … 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, or 30.

Or even listen to the sound of randomness.

Proof that 0.9 recurring equals 1

“0.9 recurring” is often written , and is equal to (where there is an infinite number of nines after the decimal point):

         

This is a commonly misunderstood concept of maths. People often think that:

• is “almost” 1, but not quite equal to it. Or,
• is the largest number that is smaller than 1.

BUT NEITHER OF THESE STATEMENTS IS TRUE! is exactly equal to 1; they are the same thing:

         

And here is the proof. Let x be equal to ,

         

Multiply x by 10,

         

Then take x away from this,

         
         

Then, by dividing both sides by 9, we find that x is equal to 1,

         

So is equal to 1.