Proof: How many consecutive THATs can go in a sentence?

Question:

How many consecutive thats can you put in a grammatically correct sentence?

Answer:

As many as you want.

Proof:

Let S_n be a grammatically correct English sentence containing n consecutive thats. (To be “consecutive”, two thats must have no intervening words. Punctuation, however, is allowed. For example, the thats in “that, that” are consecutive, while those in “that and that” are not.)

To prove the claim, I will provide examples of S_n for any integer n ≥ 0.

Consider the following cases:

• n = 0 : S₀ = This is a grammatically correct sentence.
• n = 1 : S₁ = That [i.e., S₀] is a grammatically correct sentence.
• n = 2 : S₂ = That “that” [i.e., the "that" in S₁] is part of a grammatically correct sentence.
• n = 3 : S₃ = That “that ‘that’” [i.e., the "that 'that'" in S₂] is part of a grammatically correct sentence.
• n = 4 : S₄ = That “that ‘that “that”‘” is part of a grammatically correct sentence.
• …
• n = k (k even): S_k = That “that ‘that “that ‘that … “that”‘”^…‘” is part of a grammatically correct sentence.
• n = k (k odd): S_k = That “that ‘that “that ‘that … ‘that’”‘^…“‘” is part of a grammatically correct sentence.

In other words, for any n you give me, I can give you a grammatically valid sentence containing exactly that many consecutive thats.

Now it’s your turn. Type an integer n ≥ 0 in the box and click the button.

Note: I can’t get the JavaScript to work for n ≥ 999. Probably just as well.