The Altera Centauri collection has been brought up to date by Darsnan. It comprises every decent scenario he's been able to find anywhere on the web, going back over 20 years.
25 themes/skins/styles are now available to members. Check the select drop-down at the bottom-left of each page.
Call To Power 2 Cradle 3+ mod in progress: https://apolyton.net/forum/other-games/call-to-power-2/ctp2-creation/9437883-making-cradle-3-fully-compatible-with-the-apolyton-edition
0.9999... means that you have an infinite string of 9s
IN-FI-NITE
Ever and anon, world without end, amen.
0.9999... is 1
Not for all intents and purposes, not to x degree of accuracy. In standard decimal representation they represent the same number. This is not an approximation. There is no error associated with it. They are mathematically interchangeable.
In the name of Cantor, Leibniz and Russell, amen
What, Dedekind doesn't get a mention? He had more to do with the definition of real numbers than any of the three you named!
Yeah, but even when he's stupid he gets it once it's explained. And he wants to learn more and get better. He wouldn't answer someone else's question unless he knew what he was talking about.
Originally posted by civman2000
Yeah, but even when he's stupid he gets it once it's explained. And he wants to learn more and get better. He wouldn't answer someone else's question unless he knew what he was talking about.
Nah, I agree. Just being hard on the kid.
I've run my mouth off a couple times when I had only the vaguest of clues what I was talking about.
As you've started learning more I've noticed you getting more cautious.
It happens to everybody. The more you learn, the more you know that you don't know.
Well, Apolyton is like prison. You enter the prison, thinking you are tough. You are the biggest, the meanest.. you are a murderer. You're the top dog.
But the fact is, there's always someone bigger who comes and rapes you multiple times, leaving your ass bleeding. As a result, you become humble. It is a lesson that all great prisoners learn before they themselves become the rapists.
-Pekka Truth.
In da butt.
"Do not worry if others do not understand you. Instead worry if you do not understand others." - Confucius
THE UNDEFEATED SUPERCITIZEN w:4 t:2 l:1 (DON'T ASK!)
"God is dead" - Nietzsche. "Nietzsche is dead" - God.
The OP and poll did not qualify "equal" as in regards to any specified system. Meaning that all possible evaluation systems would have to uphold the equality for it to be true given the (lack of) qualifications present. Simply proving equality in one system does not address the full spectrum of possible systems allowed by the poll as it has been defined.
As already stated, aesthetically they are not always equal. (They can be though. From infinitely far away they would appear to be the same, right?) From an efficiency standpoint (say computational time) they are not equal unless dealing with an infinite amount of them. From an expression standpoint (be that typing, speaking, ect.) they are not equal either. Even from other possible mathmatics systems (be they useful or not) they are not necessarily equal.
As there was no qualification in the poll question or OP as to the system(s) the evaulation should be limited to, the only technically correct answer is no. If the question were qualified to the point where it eliminated 99.99...% of the systems which allow for potential "no" answers, the answer could be yes.
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