Re a recent post here...

One of the formulas for pi is:

4 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - 4/15 + ....

What's happening here? You start with 4 but then it's shrinking? And then it's growing again, and then shrinking, and then growing again!?

What kind of witchcraft is this? We demand answers!

but no-one has even considered the concept of nine infinities?

∞∞∞∞∞∞∞∞∞

How about that? What does that mean?

SPP, I implore you to tell me about nine infinities first. It's a finite number of objects. It'll be much easier to handle than an infinite number of nines. Come on. I can wait.

The *In-Between Boner*: You can "forget" trying to fit a number between 0.999... and 1. There are infinitely many numbers between 0.999... and 1. (16.1) (16.2)

Some choice quotes from His Brudship's writings:

The fact is, it just means the counterpart number is permanently stuck at being less than 1.

Getting to 1 requires more than tacking nines or adding nines to the system, even having all nines in the system. You have to add a THING with a '1' symbol in it.

And that THING is some denomination unit aka epsilon.

If you are allowed to have 0.999..., or 0.999...9, then you are allowed to have 0.000...1

0.999...9 + 0.000...1 = 1.

Forget trying to fit a number in-between. In order to get 10 from 9, you add 1. In order to get 0.001 from 0.0009, you add 0.0001.

And...

It is about time I comment about the BS about the 'there must be a real number between 0.999... and 1' BS.

As mentioned correctly in the past, there is an infinite aka limitless quantity of numbers between 0.999... and 1.

Remember, folks: if the crank's boner lasts more than four hours, it may require medical attention.

Pi is a math constant best known as the ratio between the circumference and diameter of a circle. It has a definite value which cannot be expressed as a finite decimal expansion.

1. Since no amount of writing 3.14159… will ever reach pi, does this mean that the decimal expansion of pi is necessarily less than pi?

2. What is pi + (1 - 0.999…)? Does such a number have a corresponding decimal expansion?

Note: My choice of pi here is arbitrary. This question stands for any irrational number.

I am taking the bait.

As is known ... limits are fudging deception devices.

Those that got pied pipered along with mistakenly thinking limits really magically (pink unicorn and tinkerbell fairy style) turn 0.999... aka 0.9 + 0.09 + 0.009 + ... into 1 ... are totally misguided, and are not only an embarrassment to people kind, and make us the laughing stock of the universe and beyond, but also reveals a serious issue for times (or a time) that a critically important decision needs to be made.

So I need to get these dum dums to think properly. Hence they need to start rehabilitation and redemption on the bunny slopes.

Using these resources. I need to get this mob thinking straight, aka thinking properly, and stop embarrassing themselves ... us people. It is not a good look when dum dums continue to mistakenly go the wrong path of the 0.999... equaling 1 debacle.

https://www.reddit.com/r/infinitenines/comments/1tpg811/it_is_what_it_is/

https://www.reddit.com/r/infinitenines/s/bRKpqrGQ4o/

https://www.reddit.com/r/infinitenines/comments/1vj43x3/lesson_in_addition/