1 = 0.999999999999999999999999999999... ?

1=?

You seem to be confused how infinity works

yes.very.

in·fin·i·ty
a number greater than any assignable quantity or countable number (symbol ∞).

greater than a million?

about equal to the weight of your mum.

That's sufficient to emphasize that the word is being misused in this thread.

>countable
countable has a precise mathematical meaning (countable sets are actually infinite), do not use dictionary definitions when discussing technical terms

I can't believe Google gives that as a definition. Infinity is not a number. That's kind of the whole point. It's an element of the extended reals, but certainly it is not a number. Also, the proof given is genuine.

To drastically simplify this, two numbers are distinct if and only if there exists a third number between them. What number lies between these? What is the difference between the two numbers? It turns out that this is just a different way of expressing the same thing. We could write 1.000000000...=1 or 0.000000...=0 or 0.333333...=1/3.

>(countable sets are actually infinite)
Countable sets can be infinite. They aren't all infinite. The definition is not speaking about sets. Are you an undergrad that just learned this?

I agree with you on all counts, I just went to the first shitty dictionary definition to attempt to lazily point out that infinite refers to magnitude, the only infinite quantity here is the length of the decimal expansion. Same misconception in a thread last night, annoying me.

a number is a set
the only way to define "greater number" is by injections
there are different usages of countable, it's usually "countably infinite" and "at most countable" is used for infinite or countable, but usage varies and includes the one you mention
are you a high schooler who just wants to argue?

>infinity is not a number
there are plenty different numbers (ordinals, cardinals), that's really not what's wrong with the definition

>a number is a set
By some constructions.

>the only way to define "greater number" is by injections
In said constructions.

>are you a high schooler who just wants to argue?
You're the one proclaiming mathematical truth upon me for attempting to say that 0.9999999... is not infinite with a lazy definition that nonetheless is sufficient for this minor issue.

What the fuck are you talking about--genuinely I don't know. What type of number is infinity? The previous poster said it is in the extended reals (which is true) but I can't imagine it belongs to cardinal, ordinal, or nominal.

>You're the one [nonsense]
i'm the one calling you out for copy pasting a definition from google without any comment as if it fucking meant something
i don't give a fuck about whatever else you want to say, or whether you agree or don't agree with the "proof" the OP posted

0.999... isn't 1 if you include an epsilon in your number system. Just saying!

nominal?
it depends on what you mean by infinity really. most (ordinal, cardinal) numbers are infinite, all of them except for the ones that correspond to the naturals

Goddard is that you?

"In some forms of quantum gravity, the Planck length is the length scale at which the structure of spacetime becomes dominated by quantum effects, and it is impossible to determine the difference between two locations less than one Planck length apart"

>ignore 2/3 of post
Then you're calling out my laziness. I don't give a fuck. I've made my point, and a shitty non-technical definition from google was sufficient. Fuck off pedantic brainlet.

[point]
: an end or object to be achieved : purpose

>contradicting exactly nothing

[kon-truh-dikt]
to assert the contrary or opposite of; deny directly and categorically.

[bait]
food used to entice fish or other animals as prey.

Why are you bringing in physics? The number line is truly continuous such that for EVERY pair of distinct real numbers there exists a third number between them. As a matter of fact, there exist infinitely many distinct real numbers between them.

>oh he's being an idiot just like I was
>he must be baiting
right over your head, fucking brainlet

Since you appear to be genuinely stupid, my copypasta definition was meant to highlight incorrect usage of said word. Please fuck off, child.

By definition for every real number there exists a sequence of numbers converging against it, and if a sequence of rational numbers converges it converges against a real number.
Showing that 0.999... converges against 1 is trivial therefore we dont need this thread every week.

Let n = 0.99999999999999....
Suppose (for contradiction) n > 1.

Then consider 1 - n.

Since 1 > n, 1 - n > 0.

Yet there is no positive number m, with n > m > 0. Thus n is the smallest positive number. This violates the Archimedes property.

Meant 1 > n not n > 1. But the rest still stands.

well almost all math today violates the Archimedes property.

Not this shit again...

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