No. You are stuck in the explanation of limits.
0.999... is no asymptote. It is a definition/specification of a construct. This construct has a value.
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Can the definition of infinity disprove an infinite past?
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0.999... is no asymptote. It is a definition/specification of a construct. This construct has a value.
Phil Scott
Member
I've examined it, formalised it, assigned it to an equivalence class along with all other decimals, forming a complete ordered field, and with 0.999... in the same class as 1.000.... That's a damn sight more than you've ever done.
And if we don't disregard some supposed differences, what maths can we do? Please show your working. If you don't have any maths to show, if you can't do anything useful, GTFO. You're in the wrong forum and you've no business here.
Phil Scott
Member
Or for another strategy: what would make you happy?
Do you want us to stop saying 0.999... equals 1.000...?
Fine. I'll do that. Instead, how about I say this: 0.999... squeequals 1.000.... I'll agree to do all my calculus by squeequaling things instead of saying they're equals. Because sure, I concede. These things aren't really equal. They're only squeequal.
But you realise, nothing in my world will change one jot with this substitution. That's the beauty of formalising symbolically. I don't really have to care what words upset you.
Do you want us to stop saying 0.999... equals 1.000...?
Fine. I'll do that. Instead, how about I say this: 0.999... squeequals 1.000.... I'll agree to do all my calculus by squeequaling things instead of saying they're equals. Because sure, I concede. These things aren't really equal. They're only squeequal.
But you realise, nothing in my world will change one jot with this substitution. That's the beauty of formalising symbolically. I don't really have to care what words upset you.
untermensche
Contributor
No you haven't. You have immediately changed it into some other kind of notation.
In other words you have immediately transformed one thing into something else.
Yes. You have pretended it is equivalent.
You assigned it to some other thing, a class.
A capricious act.
That is a matter of utility.
Not a matter of what notations mean.
[0.999...] actually means something in that form.
It is an infinite progression that is defined as well as any infinite progression can be defined.
It can be transformed easily to something useful. Infinitely easily.
So why not just make the transformation?
But let's not immediately forget we have made a transformation.
untermensche
Contributor
0.999... is definitely an infinite asymptote in that notation.
0.9 is 0.1 away from 1.0
0.99 is 0.01 away.
As the infinite series progresses the number gets closer and closer to 1.
Phil Scott
Member
So what? I only care about the squequals anyway.
Something that's good for squequalling.
Or "squequivalent", if you prefer.
I find it squilicious.
Fine. I don't care about what notations mean. From here on, I only care about what notations squean.
We all happy now?
untermensche
Contributor
I will let other decide who has abandoned defending their position.
I know I have not abandoned mine.
You make transformations then immediately forget you have made them.
Either that or you are insanely dishonest.
A reflex.
Not a thinking mind.
All I need is a honest mind to deal with.
One that does not first pretend an infinity completes then insist it does.
Phil Scott
Member
Squawonderful!
The power of formal logic. As Hilbert pointed out, the logic works just as well if you say "beer mugs", "tables" and "chairs" instead of "points", "lines" and "planes."
That's how you do rigour, and how you do modern mathematics.
You, an incompetent wibbler, on the other hand, can fuck off.
The power of formal logic. As Hilbert pointed out, the logic works just as well if you say "beer mugs", "tables" and "chairs" instead of "points", "lines" and "planes."
That's how you do rigour, and how you do modern mathematics.
You, an incompetent wibbler, on the other hand, can fuck off.
untermensche
Contributor
When you attack a true believer's religion they get unhinged.
You are simply rounding off when it doesn't mean anything in the real world.
Infinity is a fantasy anyway.
And you don't have a fucking clue what you're doing because you cannot think anymore.
Phil Scott
Member
What are my true beliefs and my religion?
You realise I lean towards this position, right? You recall me linking that paper by David Hilbert on finitism? You remember how I agreed with you that the negative integers start at -1?
untermensche
Contributor
I tell you that you have made a transformation and not an examination and you reply with "fuck off".
Your religion is that the transformation is a necessary consequence.
When in reality the transformation is for utility, not ultimate truth.
How is it in any way possible not to agree with that?
You are hurling insults in a discussion about a human fantasy.
Phil Scott
Member
Yes. Because you're not doing maths, and have no intention of doing any maths. Take this to the appropriate forum. IOW, GTFO. Fuck off.
Nope. For starters, I haven't the foggiest clue what this means. I don't see any transformation. I see an informal idea of recurring decimals that is mathematically imprecise, but which provides a good starting intuition for the formalisation. The formalisation turns out to be fecund. Having seen its fecundity, I ditch the informal imprecision I had before, and stick to the thing that I value.
The only time I care about the original intuition is if I need to teach someone how to get here. That's not the situation here. You're unteachable.
Most people in the thread disagreed with us. Ask them. I, at least, had a mathematically coherent argument for my position. It was funny how, when I presented it, you immediately attacked it, not realising I was defending you. It was a pretty clear lesson that you're just a troll.
"Fuck off" in this case, is advice, not an insult.
untermensche
Contributor
Then fuck off!
You like to hide behind "I am telling you maths".
As if it is knowledge from heaven and not capricious decisions made for the sake of utility when things do not matter in the real world.
Morons.
They imagine a series can begin from the impossible to define.
Phil Scott
Member
It's generally good advice on this forum, I think. This banter has been amusing, but I really do need to stop wasting my time.
untermensche
Contributor
It is a waste of time because you go to "It is in the sacred texts" and refuse to go a step further.
You know all you need to know.
Actually examining what is going on is a waste of time.
Philosophy is a waste of time once one has a paycheck.
0.999... is as final as 1.000... and 1.000... is exactly the same as 1.0
0.9 is actually 0.900...
untermensche
Contributor
bilby
Fair dinkum thinkum
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And we are all oh so proud of you. Have a cookie.
There are situations where defending your position is no longer a sane thing to do. You are like one of those isolated Japanese soldiers who were still hiding out on Pacific Islands in the 1970s, refusing to believe that the war was last three decades ago.
You haven't abandoned your position. You will fight on to your last breath. But your cause was lost long ago, and cannot be saved; you are wasting your life on the defence of a long dead idea.
Imperial Japan didn't win the war; And the fact that their soldiers were still fighting long after everyone on the opposing side had stopped, does not make them the victors. It just makes them sad and deluded.
untermensche
Contributor
And we are all oh so proud of you. Have a cookie.
There are situations where defending your position is no longer a sane thing to do. You are like one of those isolated Japanese soldiers who were still hiding out on Pacific Islands in the 1970s, refusing to believe that the war was last three decades ago.
You haven't abandoned your position. You will fight on to your last breath. But your cause was lost long ago, and cannot be saved; you are wasting your life on the defence of a long dead idea.
Imperial Japan didn't win the war; And the fact that their soldiers were still fighting long after everyone on the opposing side had stopped, does not make them the victors. It just makes them sad and deluded.
This is worthless shit.
You have no position and have nothing of any merit to say about mine.
So you say this worthless shit instead.
bilby
Fair dinkum thinkum
- Joined
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And we are all oh so proud of you. Have a cookie.
There are situations where defending your position is no longer a sane thing to do. You are like one of those isolated Japanese soldiers who were still hiding out on Pacific Islands in the 1970s, refusing to believe that the war was last three decades ago.
You haven't abandoned your position. You will fight on to your last breath. But your cause was lost long ago, and cannot be saved; you are wasting your life on the defence of a long dead idea.
Imperial Japan didn't win the war; And the fact that their soldiers were still fighting long after everyone on the opposing side had stopped, does not make them the victors. It just makes them sad and deluded.
This is worthless shit.
You have no position and have nothing of any merit to say about mine.
So you say this worthless shit instead.
You might benefit from a moment's reflection as to just how incredibly accurate this is, if presented as an assessment of other people's opinions of your posts.
Of course, you won't take a moment to reflect upon that. But if you did, you might benefit.
And of course, as with so much in this thread, you should also take a moment to realize that your opinions do not change the fact that what others are saying remains true.