Do you believe the contradiction “completed infinity”?
Why don’t you do some explaining on this for a change!
Explain to me why the COMMON mathematical term for infinity is “COMPLETED! infinity”!!!
The other common term is “BOUND! Infinity”
If infinities are bounded, then they are objects and not processes, if they are unbounded, then they are processes and not objects. See?
Read message above!
Sorry for chain posting. I think mathematicians are not only arrogant, but blatantly contradicting themselves to declare infinities as bounded…
Almost out of fear or lack of self esteem, they need to believe infinity is an object to be controlled. They don’t even care about the DEFINITION of infinity, just though, to feel more powerful in their lives that they feel is insignificant
I don’t know what “completed infinity” is. Or rather, I don’t know what you in particular mean by that term. Perhaps you can help?
Note that you ignored my request to prove that the word “infinity” describes a process and not a quantity.
I don’t know what you mean by the word “object” but as I’ve said many times in the past I don’t agree with your claim that infinity is a process.
How are you going to prove that the word “infinity” refers to a process?
I am looking forward to that.
Here’s how Google defines the word “infinite”:
Nowhere is it mentioned that it refers to a never-ending process of increase.
My own opinion is that you’re confusing the process of enumerating the elements of a set with the set itself.
The set ({1, 2, 3, \dotso}) and the process by which its elements are enumarated (e.g. a computer process executing a computer program) are two different things. You are trying to deny the former and reduce it to the latter. Not gonna work.
Whether “completed infinity” is a contradiction or not depends on how you define the terms.
You define “infinity” as a never-ending process of increase and you interpret “completed infinity” to mean “A never-ending process of increase that ends at some point”. If we accept YOUR definitional premises, then yes, it logically follows that “completed infinity” is a contradiction in terms.
The problem is:
Why should we accept your definitional premises?
You have YET to prove that the word “infinity” means what you think it means.
Endless. (With a beginning)
Eternity on the other hand means without beginning or end.
Alright.
[s]I’m inclined to think the word “endless” actually means “without an end”. If “mindless” means “without a mind”, it’s only sane to assume that “endless” means “without an end”. (And not, as you say, without a beginning.)
Google appears to be in agreement with me:
But there’s a bigger problem than that.
Even if the word “endless” means “without a beginning”, I don’t see a way to apply it to sets since the word “beginning”, just like the word “end”, is not defined with respect to sets.[/s]
I misread the above quote which is why the above is struck through.
The only part that does not need to be struck through is this last bit:
Take the set of ternary digits ({1, 2, 3}). What’s the beginning of it? And what’s the end of it? Note that sets have no order, so you can’t say the beginning of this set is (1) and the end of it is (3).
So if “infinite” means “endless”, and endless means either “without an end” or “without a beginning”, what does it mean to say that a set has no end/beginning?
It’s actually sequences, not sets, that possess the ability to have a beginning and an and.
The sequence ((1, 2, 3)) starts with (1) and ends with (3). It has a beginning (the first element) and an end (the last element.)
There are sequences that have a beginning but no end e.g. ((1, 2, 3, \dotso)). Such are necessarily infinite.
Then there are sequences that have an end but no beginning e.g. ((\dotso, 3, 2, 1)). Such are necessarily infinite just as well.
And then there are sequences that have no end and no beginning e.g. ((\dotso, -3, -2, -1, 0, +1, +2, +3, \dotso)). These are necessarily infinite just as well.
But there are ALSO infinite sequences that have a beginning and an end e.g. ((1, 3, 5, \dotso, 6, 4, 2)).
Depending on how you define the term “infinite”, it might be a contradiction to say that such sequences are “infinite”. But you can’t deny that they exhibt the same property that what we nowadays call “infinite sets” do – the number of their elements is greater than every integer.
But there’s an even bigger problem than this. You’re actually arguing that the word “infinite” means more than “endless”. You are actually saying that the word “infinite” means “a never-ending process of increase”.
The problem with such a claim is that neither sets nor sequences exist in time. They do not occupy time. Thus, they can’t be one thing at one point in time and another thing (or the same exact thing) at another point in time. They have no temporal existence. Since they have no temporal existence, they cannot change (since change is a difference between two points in time.) Since they cannot change, they cannot increase in size. Their size is fixed. The set of natural numbers (N = {1, 2, 3, \dotso}) isn’t ONE size at one point in time and ANOTHER size at another point in time.
Sequences and sets, being highly abstract concepts, have no temporal existence. But there are special (non-mathematical) kinds of sets and sequences that do have such a property.
For example, the set of apples on one’s table is something that exists through time. Another example is a train – a sequence of wagons. These things have temporal existence but they AREN’T mathematical entities. And this thread is ENTIRELY about mathematics. So there’s no point in discussing them (other than to distract.)
Yet another completely irrelevant concept (:
(Which also does not mean what you think it means.)
Magnus,
You’re playing with concepts in a very sloppy way.
Infinitesimals are surreal numbers or hyperreal numbers.
You think you can use a magic wand to make a number like:
0.333pi3333…
You can’t do that.
One of the big problems you face with your arguments about infinities is that you say that if they subtract, then they can also ADD (but you only bother with subtraction because you think that’s your strongest argument.).
If you stated, 2/3rds tacked on the end of 1/3, you’d be immediately laughed out of this thread!
0.333…0.666…
Everyone would call you stupid.
How about this?
0.333…9
Same thing!
There is actually no known math utility for hyperreals, but you believe them because you can make the sentence! There are an infinite number of sentences that aren’t true:
“Existence doesn’t exist!”
There, I made a sentence! Is it true just because I made it?
Of course not!
You’re writing math that is false (hyperreals)
Is the entire point of your presence here in this thread to delcare that you’re right and that everyone else is wrong?
Sort of like what you’re doing here?
I am still waiting for you to begin addressing my points.
Oh, are we projecting now Magnus!?
You wrote an entire message about hyperreals and I responded to it!
Magnus, you’re talking over people, you aren’t talking to them.
Is
0.333pi333…
A number or not a number?
Sure, you can call me crazy for other posts in other threads (that’s what you’ve reduced yourself to), why don’t you try sticking to this thread for a change?
You know why you can’t ? Because you feel the screws of disproof slowly twisting at your skull in this thread and you don’t know what else to do.
Well, I’m still waiting for you to begin addressing my points.
I wrote a message, yes, but I am not really sure it was a message about hyperreals.
Are you sure? Can you check one more time?
You didn’t directly respond to any of the points I raised.
- I said that mathematical sets have no notion of beginning and no notion of end which means that your definition of infinity cannot be applied to them.
You said NOTHING in response to this.
- I said that it’s sequences, and not sets, that have the ability to possess a beginning and an end.
You said NOTHING in response to this.
- I said that sequences that have an end but no beginning are infinite (that they are infinite even though they have no end because the number of elements they consist of is larger than every integer.)
You said NOTHING in response to this.
- I said that sequences that have BOTH a beginning and an end are infinite (that they are infinite even though they are bounded from both sides because the number of elements they consist of is larger than every integer.)
You said NOTHING in response to this.
- I said that mathematical sets and sequences do not exist in time which implies they aren’t processes (since processes exist in time.) (And since an infinite set, being a set, is not a process, it also follows that it is not a never-ending process of increase.)
You said NOTHING in response to this.
- I said that non-mathematical sets and sequences that do exist in time are of no relevance to this topic. (Because this topic is entirely about mathematics and because mathematical entities do not exist in time.)
You said NOTHING in response to this.
And how about things I didn’t say but should have said? For example, the fact that your definition of infinity as that which is endless does not imply that infinity is a never-ending process (something you insist the word “infinity” implies.)
Perhaps you need to learn how to hold a conversation first?
So instead of directly responding to what I said, you responded to something you imagined . . . infinitesimals, hyperreals, numbers such as 0.333pi333… which I have no idea what they represent and so on.
It’s not a number because Pi is not a digit. I don’t see how this thing you came up with out of nowhere is of any relevance whatsoever. Care to explain?
Of course pi is not a digit. Pi is an algorithm. It’s a process that never ends!
Like I stated before:
In infinity, if you have a series that is every other number and use this as proof that Infinite series have different sizes!
All I have to do is write an algorithm that they all take a step back or forward like this:
If the first number doesn’t correspond then you either send all the other numbers up one step or you send all the numbers back one step.
With infinities, either way you choose will still
Have everyone holding everyone’s hand.
With finiteness, this is not possible …
Magnus,
You are treating infinite as finite!
I am waiting for you to do two things:
-
address at least one of my points
-
stop abusing “Quote” button
Here’s a song to that end:
[youtube]https://www.youtube.com/watch?v=dJxHDpKZxOs[/youtube]
Magnus,
Your last two post haven’t been discussions, they’ve been you saying, “I lost the debate and I don’t know what else to do”
You have to respond to the points that I raised.
I’ll grant you ignorance here.
In discussions on Internet forums, it’s on you to bring up AGAIN!!! that which you think I’m ignoring!!!
If you’re really lazy, just make a link to the post you think I ignored! And tell me how I ignored it
Pi is neither an algorithm nor a process. (The word “algorithm” and the word “process” mean two different things. Process is what you get when you execute an algorithm. Algorithms themselves aren’t processes. They are merely descriptions of processes.)
Most importantly, even if Pi is a terminating decimal, it still wouldn’t be a digit.
Well, I already did. Just a couple of posts ago. You even quoted it. Here it is. I made (6) different claims and you have yet to respond to a single one.