OK, so I take this to mean that you believe it is possible for a perfect, imperfection free die to exist in the real world.
OK, so you would say:
(0 <= ε < 1) AND (ε*ε = ε)
as for ε/2 being undefined, ok that’s a tough one granted (we can come back to that later), what about:
2 ε > ε ?
2 ε = ε ?
2 ε < ε ?
I cannot help but notice how the hostility and aggression keeps increasing among these guys.
A convergent one?
Sit down, count to 10, and try to think of reality.
You have been OK for the most part but you guys are starting to CONVERGE
to trolls.
2 ε > ε
ie the following concepts are also defined:
.000…0002
.000…0003
.000…0004
.000…0005
.000…0006
.000…0007
.000…0008
.000…0009
OK, now we have some “ground rules” to play with. I will try to respond later (I have some stuff to do). I assume others reading see where this might be leading so please chip in.
It must be the proximity to the real thing.
But your trolling has started to come apart at the seams, did you notice that your post #1766 was a non sequitur, pure and simple.
And hostility and aggression? You have been treated in good faith by many posters over many posts, this good faith has not been returned – if you’ve started to notice some “edge”… well, Cognitive Tide, let me introduce you to Consequences.
Sounds good.
But I will try to drill down and arrive at what I feel is a rational compromise right now.
The question of whether or not these two decimal representations are distinct members of the set has been hashed out on this thread and it seems that there is some indecision among all those concerned.
What I cannot understand, is this:
If there is indecision, what is lost in simply agreeing that 1 - .999… = ?
Or 1 =? .999…
ie it is unknown.
This would basically be the rigorous way of saying that non-zero infinitesimals are UNDEFINED
in the reals.
I just don’t see why that causes so much heartache.
Saying they ARE defined and ARE defined as zero seems contradictory to me because:
YOU CANNOT INTEGRATE OVER ZERO
“let me introduce you to Consequences.”
What are you trying to say here sir?
I need the moderator to get involved here because this is starting to sound like a real world threat to me.
Are you threatening me?
Moderator do you see what this guy is doing?
I just sent this to the moderator:
Please check my last post on the .999… = 1 thread
I have tried to be civil but The Great Unwashed has made what appears to be a threat.
I assume you are aware of Federal statutes regarding
threats made online.
If you want an ordered, complete, but non-archimedean field, there are better choices. Take the field R((X)) of formal Laurent series, for example. It’s complete (the underlying space is just a direct product of copies of R) and ordered (use the degree function plus the ordering on R), but it doesn’t have the archimedean property: n X[SUP]-1[/SUP] < 1 for all positive n. As mentioned earlier in the thread, there are also other models of the axiomatic definition of R by the Loewenheim-Skolem theorem.
The point, though, is that real numbers have a precise definition (stated many times in this thread, as well as wikipedia and elsewhere), and expressions like 0.000…01 are as meaningless as 2.001.00 or 3+./4*1 .
Just in case you don’t know, if you wish to communicate to the moderators your concern there is the little red triangle in the upper right-hand corner of my post.
Were you threatening me?
It’s no use, CT. The moderators are in the NSA’s pocket. Remember, they shut down our attempt to discuss it before.
How do you know that?
Well, that’s nice and all, but you still put forward a value that contradicts itself.
ε*ε = ε doesn’t work (and I notice you didn’t address this part of my post at all).
Moderator Note
Accusations of trolling are not permitted outside the Pit. No warning issued, but don’t do this again.
[QUOTE=Cognitive Tide]
LOL
These guys cannot step down off of their high horses into the real world.
[/QUOTE]
Moderator Note
Cognitive Tide, you have been snarky, arrogant, and obnoxious in your own posts, like the one I quoted above. I’m sure what The Great Unwashed means is that your own posting style has helped foster the hostility that you are now complaining about. I’m instructing you to dial it back or you may be liable for a warning.
Colibri
General Questions Moderator
Hmm, perhaps he is busy.
I’m guessing his calling card is pattern recognition though so here goes.
He has made what can be construed as a threat which is a violation of Federal law.
I have nowhere done this.
Are you saying my actions are more egregious?