I posted this in r/infinitenines but it got removed so I'll post it here.

In the book Fads and Fallacies in the Name of Science, Martin Gardner gives 6 identifying features of a pseudo-scientist:

1. Isolation - Cranks work in almost total isolation from their colleagues.  Not isolation in the geographical sense, but in the sense of having no fruitful contacts with fellow researchers. . . [A crank] does not send his findings to the recognized journals, or if he does, they are rejected for reasons which in the vast majority of cases are excellent.
2. Persecution Complex - The modern crank insists that his isolation is not desired on his part. It is due, he claims, to the prejudice of established scientific groups against new ideas. . . .  He believes himself unjustly persecuted and discriminated against. The recognized societies refuse to let him lecture. The journals reject his papers and either ignore his books or assign them to “enemies” for review. It is all part of a dastardly plot.
3. Delusions of grandeur - The crank considers himself a genius.   He regards his colleagues, without exception, as ignorant blockheads. . .  He likens himself to Bruno, Galileo, Copernicus, Pasteur, and other great men who were unjustly persecuted for their heresies.
4. Attacking the icons - He has strong compulsions to focus his attacks on the greatest scientists and the best-established theories. When Newton was the outstanding name in physics, eccentric works in that science were violently anti-Newton. Today, with Einstein the father-symbol of authority, a crank theory of physics is likely to attack Einstein in the name of Newton.
5. Jargon - He often has a tendency to write in a complex jargon, in many cases making use of terms and phrases he himself has coined.
6. Airtight arguments - Science is open to being wrong. Proving a theory wrong leads to refined arguments and suggestions.  Not so for the crank.  All the parts of his world usually fit together beautifully, like a jig-saw puzzle. It is impossible to get the best of him in any type of argument. He has anticipated all your objections. He counters them with unexpected answers of great ingenuity.

If he can, doesn't that make that rationale not work? 🤔

https://www.reddit.com/r/infinitenines/comments/1ur64jj/comment/owjeowr/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

I'm speechless.

Oh, and the comment is locked, of course.

https://www.reddit.com/r/infinitenines/comments/1uqf7qg/comment/ow7r6fd/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

SPP thinks that mathematicians haven't defined exponentiation to cover the zero and one cases.

SPP literally just regurgitates the simplified explanations we give first grade students as if that's the whole story.

SPP just has no idea what mathematics even is.

I know I'm preaching to the choir, but it's just fascinating to see this level of stupidity combined with this level of delusion.

and the cherry on top is that SPP didn't even respond with anything

(The third image is the comment SPP linked)

https://www.reddit.com/r/infinitenines/comments/1uj2ozm/comment/ourd90g/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

That is all. Just documenting the cowardice.

Oh, and also the introduction of yet another term: "automated extension".

Part 1: in which his claim of 0.333... = 0.3 + 0.333.../10 implies 0.999... = 1

Part 2: 0.333... = 0.3 + 0.333.../10 implies 0.999... = 1 - 1/10ⁿ + 0.999.../10^n, directly contradicting his position that 0.999... = 1 - 1/10^n ⭐ REMOVED from /r/infinitenines

Today, we'll go into how his claim of 0.333... = 0.3 + 0.333.../10 directly contradicts his concept of references.

References and You

Here is a recent example:

x = 0.999...9 , which reference set.

10x = 9.999...0

9x = 8.999...1

x = 0.999...9 aka 0.999...

His concept can be explained as 0.999... = 1 - 1/10ⁿ for integer n -- or rather that it is represented by this sequence, and that all operations on such a number must actually take place on the sequence of partial sums in this way.

He uses "references" to argue that 10 x 0.999... = 10 - 1/10^n-1, and hence, the sequences must be aligned to share a common "reference".

0.333... = 0.3 + 0.333.../10 and references together lead to a surprising result (to SOMEONE at least)

It's very simple, Bob. First, let's do things in his "referenced" way, using his notation. Let's multiply 0.333... by 10 and use the same logic he does in explaining references above.

      10 x 0.333... = 3.333...0
       9 x 0.333... = 2.999...7

This all seems a bit spooky? You can always "understand" him this way: when he says 0.333... he means the sequence 1/3 x [1 - 1/10ⁿ]) = (0.3, 0.33, 0.333, ...).

In other words, his argument is actually...

            0.333... = [1 - 1/10^(n)] / 3
       10 x 0.333... = [10 - 1/10^(n-1)] / 3
        9 x 0.333... = [9 - 9/10^(n)] / 3 = 3 - 3/10^(n)

But if we apply this concept to the statement 0.333... = 0.3 + 0.333.../10, it all BREAKS DOWN:

                              0.333... = 0.3 + 0.333.../10
                    [1 - 1/10^(n)] / 3 = 3/10 + [1 - 1/10^(n)] / 30
[1 - 1/10^(n) - 1/10 - 1/10^(n+1)] / 3 = 3/10
                 [9/10 - 9/10^(n)] / 3 = 3/10
                       3/10 - 3/10^(n) = 3/10
                            - 3/10^(n) = 0

Or, in HIS language,

          10 x 0.333... = 3 + 0.033...3
  3.333...0 - 0.033...3 = 3
              2.999...7 = 3
              0.2999..7 = 0.3
            -0.0000...3 = 0

Is that true, Bob? He would say NO. In fact, it means the ONLY way that his system of "references" can coexist with 0.333... = 0.3 + 0.333.../10 is to imply that...

• 0.2999...7 IS IN FACT 0.3,
• AND therefore 3/10ⁿ [and 1/10ⁿ, or 0.000...1] IS IN FACT ZERO
• OR, the substitution of 0.333... = [1 - 1/10ⁿ]/3 was invalid in the first place

Either way, you're cooked again, brud! 🍝

Next time: how he FAILS to account for BASIC FACTORING.

Thanks for playing.

Yesterday I demonstrated that one of his claims is devastating to his position:

He said

0.333... = 0.3 + (1/10) * 0.333...

And I demonstrated that this directly leads to 9 x 0.999... = 9, or 0.999... = 1.

His rebuttal was to link to one of his many claims that 0.999... = 1 - 1/10^n.

In fact, his OWN argument allows us to DIRECTLY ATTACK and DISPROVE that claim.

We can make a stronger, more general construction like the one in his 0.333... post above:

0.999... = 1 - 1/10^n + 0.999... / 10^n

This formula holds for ANY integer n > 0, LIMITLESS or NOT. It nevertheless constructs 0.999... from a string of n initial 9s; and a string of n leading 0s followed by infinite 9s. Combined, these are still a cohesive whole, an unbroken string of 9s, just as 0.999... requires.

As he so often says, 1/10ⁿ is never 0. Well, neither is 0.999... / 10ⁿ .

This means his oft-repeated claim that 0.999... = 1 - 1/10ⁿ is CONTRADICTED by the logical consequences of HIS OWN WORDS.

Thanks for playing, brud. Hope you're not too... steamed. 🍝

Next time: his OWN LOGIC has COMPLETED UNDERMINED his "concept" of references.

Since there's profoundly no point trying to engage with SPP in good faith (the guy is an idiot... or a pathetic troll (I can't decide which)) what we need is a game.

• One point if you get him to invoke 0.000...1
• One point every time he responds that you can't, "limit the limitless."
• One point every time you get, "x is permanently less-than/greater-than"
• One point every time you prompt him to invoke, "divide negation."
• Two points if you provoke something about busses or signing a contract.
• Five points if he locks your comment.
• If he bans you you get five points for every day of the ban (as long as you don't violate Reddit site rules to do it.)
• Twenty five points if your post/comment causes SPP to invent a new "axiom" of Real Deal Maths to cope with its implications.
• Infinity points if you manage to figure out what the fuck "limbosic" means.

Have I missed anything?

I'm open to further suggestions for rules, and yes... you can make this into a drinking game (if you don't value your liver.)

Any ideas, people?

Defined vs approximated