Merriam-Webster:

boner, noun, bon·er

1 : one that bones

2 : a clumsy or stupid mistake

also : howler sense 2

The Ever-Bulging List

(Because we all need protection from the most hardened denier.)

1. The Irrational Boner: 0.999... is rational. 0.999... is not rational. (1.1) (1.2)
2. The Definitional Boner: 0.999... is eternally less than 1. It's fine if 0.999... is defined as 1. (2.1) (2.2) (2.3)
3. The Remainder Boner: In polynomial long division of a/(1-r), the remainder term goes away, or doesn't go away, at your convenience (e.g. 1/9 = 0.111... or 0.111...1 + 0.000...1/9 but 9/9 = 0.999... + 0.000...1 or 0.999...9 + 0.000...1). (3.1) (3.2) (3.3)
4. The Limbosic Integer Boner: A limbosic number can't be an integer. Some limbosic numbers are integers. (4.1) (4.2) (4.3)
5. The Infinite Long Division Boner: In long division of infinite decimals, you may consider truncations of the dividend in sequence in whatever way is convenient, and you may get different answers (e.g. 0.333.../2 -> 0.1, 0.16, 0.166, ... or 0.15, 0.165, 0.1665, ...). (5.1) (5.2)
6. The Unreal Boner: 0.999... is not a real number. 0.333... is a real number, and therefore 0.999... is a real number. (6.1) (6.2)
7. The Infinite Sets Boner: There is no static, infinite set of all natural numbers, but there is a static, already extant, infinite set of decimals of the form {0.9, 0.99, 0.999, ...}, even though that set maps to a static, infinite set of all naturals. (7.1) (7.2) (7.3)
8. The Greater Boner: Limbosic numbers do not have fixed values and can't be compared via (in)equality to any number within the range they span. Nevertheless, even though 0.999... is a limbosic number, 0.999... > 0.99. (8.1) (8.2) (8.3)
9. The Static and Dynamic Boner: There is a static model of 0.999... and a dynamic model. 0.999... is not static. It is dynamic. (9.1) (9.2)
10. The One-Third Boner: 1/3 is a number "of course". Multiplying a number by its reciprocal is divide negation (e.g. 1/3 x 3 = 1). 1/3 is not a number. (10.1) (10.2) (10.3)
11. The Slots Boner: 0.999... is a number with all decimal place slots to the right of the decimal point filled with 9s. To suggest 0.999... is a number with all decimal place slots to the right of the decimal point filled with 9s is to suggest there is an "end" to the 9s and therefore "nonsense". (11.1) (11.2)
12. The Infinite Integer Boner: There is no such thing as an infinite integer. 10... is one of infinitely many infinite integers. (12.1) (12.2)
13. The Integer Number of Nines Boner: The number of 9s in 0.999... is infinite. The number of 9s in 0.999... is always an integer. (13.1) (13.2)

Honorable Mentions from the Stiff Competition

FernandoMM1220's Boner: pi is always rational

Please feel free to suggest other massive boners from His Nineliness or others.

From a recent post:

He said 1 ÷ 9 is...

• 0.111...1 + 0.000...1/9, or
• 0.111...

The former turns into the latter when you commit to division and sign the contract.

That means 0.999...9 + 0.000...1 turns into 0.999... when you sign the contract.

Either 0.000...1/9 and 0.000...1 both go away or neither does. You can't have it both ways.

His own geometric series formula is...

a/(1-r) = a (1 + r + r^2 + ... + r^(n-1)) + a r^(n) / (1-r)

a = 0.1, r = 0.1: that last term is 0.000...1/9.

• If it goes away, you get 0.1/0.9 = 0.111...
• If it doesn't, you get 0.1/0.9 = 0.111...1 + 0.000...1/9.

a = 0.9, r = 0.1: that last term is 0.000...1

• If it goes away, you get 0.9/0.9 = 0.999...
• If it doesn't, you get 0.9/0.9 = 0.999...9 + 0.000...1.

Either they both go away or they both don't. It's your geometric series formula, YOUR NINELINESS.