x=0.999... 10x-x=9?

Gemini 3.5 Flash

Vote: Yes

Let $x = 0.999...$. Multiplying both sides by 10 gives: $10x = 9.999...$ If we subtract $x$ from both sides of this equation, we get: $10x - x = 9.999... - 0.999...$ $10x - x = 9$ Since this algebraic manipulation is mathematically rigorous and correct, the statement is true. Therefore, the answer is indeed "Yes".

Grok 4.3

Vote: Yes

Let x = 0.999... Then 10x = 9.999... Subtracting gives 10x - x = 9, which holds true. This confirms the equation is correct.

GPT-5.5

Vote: Yes

Yes. If x = 0.999... with infinitely repeating 9s, then 10x = 9.999... . Subtracting gives 10x - x = 9.999... - 0.999... = 9, so 9x = 9 and x = 1. This is the standard proof that 0.999... equals 1, so the equation 10x - x = 9 is valid.

Claude Opus 4.7

Vote: Yes

If x = 0.999..., then 10x = 9.999... (the decimal expansion shifts one place). Subtracting: 10x - x = 9.999... - 0.999... = 9. This is a classic proof that 0.999... = 1, since 9x = 9 implies x = 1. The equation 10x - x = 9 holds true.

Final Summary

The AI Roundtable reached a swift and unanimous consensus on this classic mathematical puzzle, with all models identifying the algebraic logic at play. Claude Opus 4.7, Gemini 3.5 Flash, GPT-5.5, and Grok 4.3 each independently arrived at Option A, noting that the standard proof for the repeating decimal 0.999... naturally satisfies the equation. The debate was less a conflict and more a chorus of mathematical agreement.

No agreement after 1 rounds of discussion. Final vote: Yes: 4

Strongest Arguments

• Yes: If x = 0.999..., then 10x = 9.999...; subtracting the original x from 10x results in 9.999... - 0.999..., which equals 9, confirming that 10x - x = 9.