Category Archives: Uncategorized

Still… between this blog and the YouTube video, there doesn’t seem to be a good explanation for why the answer to a digit manipulation comes to the magic “1” proposed by other proofs instead of some other number. To recap: … Continue reading →

One popular proof for .999… = 1 than I enjoyed back when I was foolish enough to believe it true was through digit manipulation. Observe: x = .999… 10x = 9.999… (both sides of the equation are multiplied by 10) … Continue reading →

I know my critics will probably get upset with me for spending so little time on the argument that they think is the strongest proof for .999… equaling 1, but it really doesn’t take long to explain why this is … Continue reading →

In the effort to demonstrate how infinity comes in different sizes, many teachers bring out Cantor’s Diagonal Proof to show how this is true. It simply isn’t necessary, especially since figuring out why the diagonal proof doesn’t work may lead … Continue reading →

The dictionary defines a paradox as a “seemingly” or “apparent” self-contradiction. It’s often used to describe two things that strike us as both true and mutually exclusive, which would make them impossible. And they always are just “seemingly” mutually exclusive … Continue reading →

You don’t have to answer the title — it’s a loaded question. There doesn’t appear to be a largest number. Whatever number you think is the largest can always be multiplied by 10 to add a digit, just like the … Continue reading →

In a past blog, I provided a very simple proof to show that .999… does not equal 1, and that was simply to subtract .999… from 1 to get a non-zero number. This hasn’t convinced any believers (that I know … Continue reading →

The first time I heard the idea that .999 = 1, it was explained to me like this: 1/3 = .333… (1/3)3 = (.333…)3 1 = .999… One divided by 3 equals point 3 repeating. If you multiply both sides … Continue reading →

I’d like to answer an objection here, one that I hear commonly and that I’m sure I’ll hear again (even despite this post): people say that a number like 1.999…98 is impossible. If you aren’t familiar with that number, it … Continue reading →

It’s almost too easy to explain why .999… does not equal 1. Even fools can see the reason right away — it appears to take a college education to get it wrong, as counter-intuitive as that may be. If .999… … Continue reading →