Pizza proof 0.999... = 1

If you can slice a pizza, you can do math :)

James Tanton, March 2008 CMJ proof without words

@MathVisualProofs short 0.999999… = 1 (using a circle)

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[random-uploaders]

I'm more worried that nine-sided pizzas exist

[fenhen]

I feel like this isn’t a proof that would convince students, because the step of “eventually you’ll have the whole pizza” requires a leap about the nature of infinity.

[thenarstar]

"Hello Domino's"
"Hi! Can I get a nine sided pizza please?"
* hangs up *

[charleslivingston]

Why confuse things but using a nine-sided pizza. Why not just use a circle?

The number of sides doesn't show up in any of the terms — just the ratio of how much you scaled it down from the previous shape

[BryndanMeyerholtTheRealDeal]

This also proves that any terminating decimal has two forms, one repeating, and one not (like 0.3 is equal to 0.2999 repeating)

[huzefa]

I like this demonstration very much....
It just proves how x =
So 10x – x = 9x
9.999 – 0.999 =
9 = 9x
x = 9/9 = 1

[smylesg]

Looks more like a limit that approaches 1, but I'll give it to you.

[jinxixteen]

Problem, if you go on to infinity, then you won't ever slice the whole pizza, since you're allways slicing into 9ths

[chupitofresco]

You missed the of cheese stuck on the knife

[Blockenheimer]

you know how one third is .333?
so if I cut a pizza in 3 slices, all the slices together will be .999
If you're wondering where the extra .001 is, you will find it on the knife

[mymatemartin]

the poor tenth person will forever miss out on a slice. 😁

[MrTeniguafez]

I remember when I was a kid, my dad made it easy for me to understand by pointing out there's no number between 0.999... and 1.

[NautilusMakesMusic]

I don't understand any of this but it's keeping my attention somehow

[atomman]

The 0.01 is in the knife we used to cut the pizza

[KeeBaud]

The problem with this proof is that some people will argue that there is always a hole in the middle, which breaks the intuitive nature of this proof.

[DavidFrankland]

Next time I order a pizza I'm going to get them to cut it into an infinite number of slices and see how long it takes them

[Spasm]

I'm not an English native so I'm sorry because I don't know how certain things are named in English.
Base concept here is that "0.9 + 0.09 ... = 1"
But that's not "equal" in this equation, because that comes from numerical sequences, which means that in your case it's "heading to 1" but will never be 1!
So basically what you're doing here is "meh, close enough, it's 1".

Imagine another scenario equal to this one:
If I divide pizza by half an infinite amount of times, so each slice is "heading to 0".
So with your logic, if it's heading to 0 then I assume it's 0.
Conclusion:
Don't divide your pizza by half too many times because you gonna make it disappear completely.

[Hogscraper]

Seems like someone took the real pizza proof, divide a circle into thirds, turn the fractions into decimals then add those 3 into and decided that it needed to be way more complicated and no longer resemble a pizza.

[gabrielbarrantes]

Not this again man, that doesn't prove it, this proves that 0.9, 0.99, 0.999, ... converges to 1. By definition is not an infinite sum, is a completely different object. Proving that statement requires proper definition of real numbers, in this case using "decimal expansions with infinite decimals" and then it will follow from the definition.

[Araqius]

Just try to do square root 0.999... by hand.
You will find that the answer is 0.999...
The only number that get itself back when square rooted is 1 and 0.