Thread: .999~=1!

Originally Posted by PhilosopherStoned

The fact that it doesn't have a value at infinity is really just a defect of the non-projective coordinates.

But it is exactly why 0.999~ does not equal 1.
It is used for all intents and purposes to equal 1.
But by its very definition it "infinitely approaches 1, never reaching it".

So I don't get why this whole debate ever comes to be.

0.999~ is just that. And 1 is just that.
They are not equal, but the former is rounded to the latter.
Because during application the difference is negligible.

However, when you say "something is equal to something else", that isn't about application.
It's about static conditions.
So when saying 0.999~ is equal to 1, you're saying two different values (no matter how small the difference is) are the same.

And that's just obviously bogus.

In other words, you don't even have to know any math or anything about parabolas or any such to realise that if two different values are defined to be different, they are different. Doesn't matter how they are applied in calculations and all. Conceptually (not mathematically), they are different.

Originally Posted by Merlock

But it is exactly why 0.999~ does not equal 1.
It is used for all intents and purposes to equal 1.

two different contexts.

Originally Posted by Merlock

But by its very definition it "infinitely approaches 1, never reaching it".

You're confusing the definition of an infinite sum with an infinite sequence.

Originally Posted by Merlock

So I don't get why this whole debate ever comes to be.

because people that know nothing about math like to feel like they have any input to offer.

Originally Posted by Merlock

0.999~ is just that. And 1 is just that.

precisely. They are both equal to 1.

Originally Posted by Merlock

They are not equal, but the former is rounded to the latter.
Because during application the difference is negligible.

See above. Is there something you don't understand? I would be more than willing to help you.

Originally Posted by Merlock

However, when you say "something is equal to something else", that isn't about application.

It's about static conditions.

from a formal perspective, all mathematics is about static conditions..

Originally Posted by Merlock

So when saying 0.999~ is equal to 1, you're saying two different values (no matter how small the difference is) are the same.

see the proof in my previous post.

Originally Posted by Merlock

In other words, you don't even have to know any math or anything about parabolas or any such to realise that if two different values are defined to be different, they are different. Doesn't matter how they are applied in calculations and all. Conceptually (not mathematically), they are different.

reread my post. .9999...... is defined to be the limit of the sum which is 1. You don't need to know anything about math but it helps if you want to understand stuff. This is math, not literature. There is one truth value that can be assigned to any statement.

Hope that clears stuff up.

Originally Posted by PhilosopherStoned

Hope that clears stuff up.

It doesn't clear stuff up, since you yourself agreed with my stance.

Originally Posted by PhilosopherStoned

The fact that it doesn't have a value at infinity is really just a defect of the non-projective coordinates.

You agree that it's a fact that there is no value for it at infinity.
No value. Not 1.
And if it isn't 1, it isn't equal to 1.

Doesn't matter how it's applied. Conceptually, it never reaches 1.

Originally Posted by Merlock

It doesn't clear stuff up, since you yourself agreed with my stance.

Quote me agreeing with your stance. Do you mean about it being static? you're right. That has no bearing on the question at hand.

Originally Posted by Merlock

You agree that it's a fact that there is no value for it at infinity.
No value. Not 1.
And if it isn't 1, it isn't equal to 1.

Doesn't matter how it's applied. Conceptually, it never reaches 1.

I was talking about an algebraic curve which is a function. It was an aside for invader. It's a cool fact. This is totally different.


Here's another way to think about it from a topological perspective. The real numbers form a continuum. This means that given two real numbers, a and b, I can always find a third real number c, such that a < c < b. I can always stick a number in between them. All you have to do to prove that .9999...... is not equal to 1 is find some number that you can stick between the two.

here's yet another way to think about it. What's 1 - .99999999.........?


essentially what you are doing is saying that 4 + 1 =/= 3 + 2 because I am writing them differently. 1 = 1.000000....... = 1 + .0 + .00 + .000 + ....
is an infinite sum as well. It just has trivial terms after the first but is really just another way of writing .99999..... = 0 + .9 + .99 + .999 + .....

Originally Posted by PhilosopherStoned

The real numbers form a continuum. This means that given two real numbers, a and b, I can always find a third real number c, such that a < c < b.

This is what I meant when I said I don't understand why this whole debate comes up.

What you said in the above quote has no relevance whatsoever.
There is simply no need to prove or disprove that 0.999~ = 1.
By definition, 0.999~ infinitely reaches towards 1 but never gets there.

And calculations like those limits up there or formulating things like a < c < b...
None of it matters.
If something is defined specifically to never be equal to something else...it isn't.

In other words, what I mean to say is that I don't see any reason for any of the above proof to even exist.

And as such, I shall withdraw from this topic so as to avoid taking part in trying to prove or disprove something, heh. Just wanted to get my position out there, as it's always misinterpreted as me trying to disprove something. When in fact, I fully realise that 0.999~ and 1 are two different values by definition, and I simply wonder where anyone got the idea to start a debate about their equality.

It's like someone seeing 5 apples lying near a pile of 476 metal bolts, then suddenly getting up and stating, "I'm going to prove that 5 = 476!"

To all of you who can't understand how .999~ = 1, keep in mind you can't argue math in words.

So, provide a formal proof showing .999~ =/= 1 or GTFO.

Edit: Also, I find it hilarious that this was re-posted in Senseless Banter.

Ahrgh!

These threads are like an infinitely recurring nightmare.

The .9999~ is not equivalent to the value that comes after the decimal in 9.9999~.

NO.

But it is exactly why 0.999~ does not equal 1.
It is used for all intents and purposes to equal 1.
But by its very definition it "infinitely approaches 1, never reaching it".

NO.

Numbers don't APPROACH anything, they are FIXED values. Note that 0.999~ represents an INFINITE string of 9s, not ROUGHLY 0.999.

The fact is that it has been proved in the first post and you can't argue, as has been said above, with a mathematical proof. Especially not with words and analogies.

it's widely accepted in mathematics that the function that represents a parabola can approach but never be equal to it's asymptote at any point on the graph, even though it can close the 'space' to infinitesimally small distances.

Lord, you sound extremely intelligent. I'm in awe at the largeness of your words.

Except parabolas don't even have any asymptotes.