Thread: .999~=1!

To prove it in a different way, you can actually use the formula for calculating the sum of an infinite geometric progression. The initial term would be 0.9 and the ratio would be 0.1:

S = (0.9 + 0.09 + 0.009 + ....)

S = a1 / (1 - q)

S = 0.9 / (1 - 0.1)

S = 0.9 / 0.9

S = 1

Yesh that's a nice way, or you can even go back to the basics of proving the GR formula:

S = 0.9 + 0.09 + 0.009 + ...
0.1S = 0.09 + 0.009 + 0.0009 + ...
S - 0.1S = (1 - 0.1)S = 0.9S = 0.9
=> S = 1

It really comes down to math vs. logic. Math tells us that it does equal 1, but logic tells us just the oposite.

As Kromoh said, you're talking about intuition, and the problem is that intuition is subjective, unlike mathematics. As a matter of fact I find it totally intuitive that 0.999... is equal to 1, as the number is infinitely close to 1 and hence equal; I do not understand anybody who finds the opposite intuitive.

That's why we have mathematical proof anyway. Sometimes results are surprising.

I wasn't expecting serious answers in SB -_-

Originally Posted by hellohihello

I wasn't expecting serious answers in SB -_-

I may be guilty on that one +.+

0.999~ = 0.9 actually. :V

You can't comb the hair of a spherical dog without introducing a part

The complex numbers are isomorphic as a ring to R[x]/(X^ + 1)

A vector space is just a ring homomorphism from a field into the endomorphism ring of an abelian group

A torus has zero global curvature

You can't comb the hair of a spherical dog without introducing a part

This is also true of spherical cows.

Another interesting fact about spherical cows is that you can split the cow into a finite number of pieces, reassemble it, and you'll have two new spherical cows of exactly the same volume as the first one.

This assumes that the cows are continuous.

When I saw the post I though "well, that's all wrong. It can't be"
Then I actually read some of the posts, and it makes perfect sense. Why do people continue to deny it? >.<

Originally Posted by khh

When I saw the post I though "well, that's all wrong. It can't be"
Then I actually read some of the posts, and it makes perfect sense. Why do people continue to deny it? >.<

And that's how math works. Isn't it pretty? You really can't disagree.

Actually I disagree with the axiom of associativity.

Prove it now, dick.

And that you want to work your way through all those homeomorphisms

And udders. :V

let's see, associativity....that's (a + b) + c = a + (b + c). It's gonna take me a second and I don't have my book that covers the fundamentals so I might not be able too. I'll do it in pieces.

Originally Posted by Xei

As a matter of fact I find it totally intuitive that 0.999... is equal to 1, as the number is infinitely close to 1 and hence equal; I do not understand anybody who finds the opposite intuitive.

I might jump off a cliff after I open up this can of worms with you again, but how does the number get (not that it is moving) infinitely close to 1? Apparently it does, but how? Infinity goes on forever. At any 9, you can move to the next 9, and 500 quadrillion googol octillion 9's later. The 9's extend forever. It has no end, so how is it 1? It just sounds so much like talking about the end of space. 1 is a very exact number.

0.999... is also an 'exact' number (being the same number, 1).

how?

Infinity goes on forever.

That's the answer really. Each consequtive 9 decreases the difference between the number and 1 by a factor of 10. You do this infinite times and you've decreased the difference by a factor of infinity; i.e. there is 0 difference.

I think you're asking at what point leading up to infinity is it 0; there is no point. That's the whole point of infinity, it isn't a number as such. It just represents what would happen if you did it again and again and again forever. You can't in practice, but it's just a concept.

The above is all intuitive however. The real answer to your question is simply the mathematical proofs which have been offered. Mathematics is abstract. Think what would happen if you tried to discuss the Banach–Tarski paradox in this way; it doesn't work.

I sort of see what you are saying, but it's that concept of infinity that is so baffling. Like, if you traveled an infinite distance in one direction, you would go through all of space in that direction. That makes sense in a way, and theoretically it is true, but it is still a big WTF since space does not end.

I remember proving this in Algebra 2. Fun.
inb4lock