echeadle (85) [Avatar] Offline
Could you point me to a source that has longer explanation about the sum of two numbers found on page 4? I am missing something. It has been a long time since I did algebra, but the sum of two odd numbers is 2(n+m+1)? If I assign two odd numbers n=3 and m=5. The sum is 8. Using your equation 2(3+5+1) = 18. I assume the mathematics is some sort of proof for all numbers, but it has been a very long time since I took math and it is very hazy. A pointer to another source would be enough. Proving this point is not important to this book, but it would help those people who haven't taken a math course in 40 years. smilie

I am only into the book a few pages, but after reviewing the material, I am very interested in seeing the next chapters.
Nishant Shukla (52) [Avatar] Offline
Hi echeadle,

Great question!

For any integer n, the formula 2n+1 produces an odd number. Moreover, any odd number can be written as 2n+1 for some value n.
So the number 3 can be written 2(1) + 1. And the number 5 can be written 2(2) + 1.

So let's say we have two different odd numbers 2n+1 and 2m+1, where n and m are some integers.
Adding two odd numbers together yields (2n+1) + (2m+1) = 2n + 2m + 2 = 2(n+m+1).
This is an even number because 2 times anything is even.

Here's a great resource to see another explanation:

I'll improve the wording in the book.
echeadle (85) [Avatar] Offline
It has been too long since I took a math class that included mathematical proofs. I completely understand the concept now that you wrote:

So the number 3 can be written 2(1) + 1. And the number 5 can be written 2(2) + 1.

I like this kind of short sentence, and something like it easily clarifies the concept you are striving for.

Late night and reading stuff in a hurry does not help in understanding mathematical proofs.

Thank you for taking time to clarify.