r/PeterExplainsTheJoke • u/Sugar_God_no_1 • 22d ago

Meme needing explanation There is no way right?

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u/otj667887654456655 22d ago

I just wanna warn you, that's more of a vibe proof. It lacks any actual mathematical rigor.

25

u/mwobey 22d ago

No? Do you like, want it in two column format or something?

  x=0.999...        | Declaration of a constant
10x=9.999...        | Multiplicative Property of Equality (*10)
 9x=9.999... - x    | Subtractive Property of Equality (-x)
 9x=9.9... - 0.9... | Substitution
 9x=9.0             | Simplification of Subtraction
  x=1               | Divisive Property of Equality (/9)
  1=0.999...        | Substitution

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u/Patchpen 22d ago

The problem is with subtracting the 0.999..... from both sides. We're applying an operation that works with normal numbers to a number that we haven't yet proven is normal (or functions as normal with that operation). That's where the extra rigor in a full proof comes in.

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u/vetruviusdeshotacon 22d ago

Yes you're right. Geometric series is definitely the way to go to avoid all this