I can’t even start writing this without getting a big grin on my face, or at least one of those eyes twitching. Why? Because 5 is the smallest number that is both positive and negative! For instance, the number 5 is either the largest or smallest number with a positive value, but it’s still a positive number. A positive number does not mean it is good, the negative does not mean it is bad.
So how do we determine which is which? Its very simple, its called Euclid’s Theorem. If you can write a 5 digit number down on a piece of paper, and you can’t make any mistakes, you will have found the smallest number.
Euclids Theorem is what makes 5 the smallest number. It means you can write a number down in 5 pieces so you have a positive number, but you cannot make any mistakes, and so you can use this number to tell you it is smallest. The smallest number is that number whose digits sum to 5, which is 5.
You can find the smallest number using any method. But what makes 5 the smallest number is the fact that there aren’t that many numbers smaller than 5. If there were, there would be more digits to make a number smaller. So what makes 5 the smallest number is that it can’t be written down in fewer pieces.
If 5 is the smallest number, then 5 must be the smallest number because any number smaller than 5 is already a multiple of 5. This means that 5 must be the smallest number because if it was smaller than 5 that means that it could not be written down using smaller pieces. If you can use fewer pieces to write down 5, then it must be the smallest number.
5 is the smallest number because it is the smallest number that has more than one digit. If you can use more pieces to write down 5, then it must be the smallest number. But 5 cannot be written down using more pieces because then it would be a multiple of 5. So 5 is the smallest number because it is the smallest number that is not written down using more pieces.
It’s a fascinating idea. But the biggest problem is that it’s not even a question. If you have a really small number, then it’s actually really difficult to use all the pieces to write it down. The smallest 5 digit number that you can write down using a set of 9 pieces is 5. If you can write 5 using fewer pieces, it’s not the smallest numbers. But 5 cannot be written down using fewer pieces because then it would be a multiple of 5.
Its not too bad if you’re writing 5 using just 5 pieces. But if you’re using 5 pieces to write 5 you still haven’t written 5. Now you’re writing 5 using 4 pieces. You can’t use 4. You can’t use 3, 2, 1. Only 3, 2, 1. And so on. That’s why its not a question. The smallest number that a person writes using a set of 9 pieces is 10.
In other words, you can write the smallest number using fewer pieces than it takes to write the smallest number using less pieces. And this is why our friend “the smallest number” is so important. One of the main principles of the math we discuss in this book is that a small change can have a big impact on a calculation. So if I change the order of multiplication to the left, I can change the value of the result.
This principle is so important because it helps us understand a lot of things. I’m not sure if you can guess right now what this is, but it’s a really important principle. For example, if I change the order of multiplication to the left, I can change the value of the result by 1/2.