Does PERFECT = IMPERFECT ?
 

I've decided to share my Sunday musings with a few more people other than myself, so here I come !

Does Perfect = Imperfect ?

A typical answer may be " of course not, silly ! ". A more reasoned response may be " no, but what are you trying to say ? ". And then, an hopeful response would be " maybe, if you consider a few limitations ". The best response is, of course, " yes, you are absolutely correct in your assertion, if it's an assertion ".

For example, does a person who stutters = a person who does not stutter. Or to be more clear, does a stuttering person stutter ? Of course, a stuttering person does not stutter !

I know this to be true, because if you ignore all the malformed words or attempts at word formation from a stuttering person, that person speaks perfectly, or just as well as I do, because I do not stutter.

So, by induction, I think, PERFECT = IMPERFECT , if you ignore that which may lead you to think that PERFECT <> IMPERFECT ! ( more than or less than, but not equal ).

And now another " prime " example of this kind of thinking is this:

ZERO = INFINITY

Be careful here, there is a trapdoor !

Zero is isomorphic to infinity with respect to division and multiplication. Equal? no...infiinity is not an identity operator for addition or subtraction.

And certainly noone here would confuse an imperfect number with a perfect number...especially an ODD perfect number. :smile: :leaving:

[QUOTE=9021951;275451]I've decided to share my Sunday musings with a few more people other than myself, so here I come !

Does Perfect = Imperfect ?

A typical answer may be " of course not, silly ! ". A more reasoned response may be " no, but what are you trying to say ? ". And then, an hopeful response would be " maybe, if you consider a few limitations ". The best response is, of course, " yes, you are absolutely correct in your assertion, if it's an assertion ".

For example, does a person who stutters = a person who does not stutter. Or to be more clear, does a stuttering person stutter ? Of course, a stuttering person does not stutter !

I know this to be true, because if you ignore all the malformed words or attempts at word formation from a stuttering person, that person speaks perfectly, or just as well as I do, because I do not stutter.

So, by induction, I think, PERFECT = IMPERFECT , if you ignore that which may lead you to think that PERFECT <> IMPERFECT ! ( more than or less than, but not equal ).

And now another " prime " example of this kind of thinking is this:

ZERO = INFINITY

Be careful here, there is a trapdoor ![/QUOTE]

Just what we need. Another nitwit crank.

Go back to school. Study very hard. When your IQ reaches 50, SELL.
You will make a profit.

[QUOTE=Christenson;275458]Zero is isomorphic to infinity with respect to division and multiplication.
[[/QUOTE]

Total horsesh*t. This is gibberish.

@ 1min 16sec
[YOUTUBE]BqxmLpxUncA[/YOUTUBE]

[QUOTE=R.D. Silverman;275463]Total horsesh*t. This is gibberish.[/QUOTE]

Let me re-phrase: (I've been working problems out of Leveque's number theory book, but didn't quite get my proper mathematical hat on....)
Under the map R*-->1/R*, where R* is the real numbers with infinity added,
the operations of multiplication and division are preserved, with zero mapped to infinity and vice-versa.
This map is 1 to 1 and onto. and therefore is an isomorphism.

What did I miss? Surely isomorphisms aren't limited to rings, though they may be more useful there...

[QUOTE=9021951;275451]So, by induction, I think, PERFECT = IMPERFECT , if you ignore that which may lead you to think that PERFECT <> IMPERFECT ! ( more than or less than, but not equal )[/QUOTE]

Yeah. And 1 = 2, if you ignore the extra 1 that is causing the 2 to not be equal to 1. :huh:

EDIT:- btw, there is a poll in there, if anyone cares.

[QUOTE=9021951;275451]Does Perfect = Imperfect ?[/QUOTE]Yes it does ... but only if you live in Wonderland with Alice. And you can even extend your argument to "anyOneThing = anyOtherThing", you just have to make sure you ignore all the things where anyOneThing != anyOtherThing and, eureka, you will find that anyOneThing = anyOtherThing. :loco:

[size=1]For the poll - I was looking for the fifth option: Wish I hadn't clicked on this topic.[/size]

You need to watch Flatlander's video up there....really...

[QUOTE=Christenson;275471]Let me re-phrase: (I've been working problems out of Leveque's number theory book, but didn't quite get my proper mathematical hat on....)
Under the map R*-->1/R*, where R* is the real numbers with infinity added,
the operations of multiplication and division are preserved, with zero mapped to infinity and vice-versa.
This map is 1 to 1 and onto. and therefore is an isomorphism.

What did I miss? Surely isomorphisms aren't limited to rings, though they may be more useful there...[/QUOTE]

You need to state that you are working in the EXTENDED REALS and not
the REALS.

[QUOTE=Christenson;275509]You need to watch Flatlander's video up there....really...[/QUOTE]I've no flash player here. Perhaps you could explain what you are referring to?

[QUOTE=retina;275520]Perhaps you could explain what you are referring to?[/QUOTE]
I don't know to what you refer.
(Brief Encounter)

[QUOTE=retina;275520]I've no flash player here. Perhaps you could explain what you are referring to?[/QUOTE]

As exemplified in a scene from Toy Story 2: Stationary pylons create turbulence to Laminar flow. Moving pylons create chaos?

[QUOTE=imwithid;275535]As exemplified in a scene from Toy Story 2: Stationary pylons create turbulence to Laminar flow. Moving pylons create chaos?[/QUOTE]

More than that: Only by a great bit of good fortune do the toys make it across the street in one piece, and they unknowingly leave a great deal of chaos behind them.... so it goes when black is confused with white....or zero with infinity...remembering that the isomorphism breaks down when addition or subtraction is considered.

The video is fun to watch....think of Charlie Chaplin in "Safety Last" for the inspiration used....

A few questions, and a possible retort !
 

[QUOTE=Christenson;275471]Let me re-phrase: (I've been working problems out of Leveque's number theory book, but didn't quite get my proper mathematical hat on....)
Under the map R*-->1/R*, where R* is the real numbers with infinity added,
the operations of multiplication and division are preserved, with zero mapped to infinity and vice-versa.
This map is 1 to 1 and onto. and therefore is an isomorphism.

What did I miss? Surely isomorphisms aren't limited to rings, though they may be more useful there...[/QUOTE]

Is that LeVeque's "Topics in Number Theory, Volume One"? This does not seem to be covered in " Elementary Theory of Numbers " ( Dover edition, 1992 ).
I sense that Cantor and Dedekind are lurking nearby. If I understand what you are writing, does that mean I have an IQ > 50. If so, should I truly sell as previously advised?

Help !

[QUOTE=9021951;275451]I've decided to share my Monday musings with a few more people other than myself, so here I come !

Be careful here, there is a trapdoor ![/QUOTE]

Did everyone choose to ignore the paradox ? A trapdoor <> a trapdoor, if one knows that it exists. It can only exist if one is starting to fall through it, and with no knowledge of its existence until that time or later.

Sheesh !

PS I told you that there was a trapdoor !
PPS Why do I keep spinning in circles ?

[QUOTE=9021951;275558]A trapdoor <> a trapdoor, if one knows that it exists. It can only exist if one is starting to fall through it, and with no knowledge of its existence until that time or later.[/QUOTE]So if we follow your "logic". Once we begin our fall through the trapdoor -> then we have knowledge of it -> and then it ceases to exist (because of our knowledge of it) -> and therefore we are no longer falling through a trapdoor (since it doesn't exist). So what are we falling though again?

So What Gives ?
 

[QUOTE=retina;275562]So if we follow your "logic". Once we begin our fall through the trapdoor -> then we have knowledge of it -> and then it ceases to exist (because of our knowledge of it) -> and therefore we are no longer falling through a trapdoor (since it doesn't exist). So what are we falling though again?[/QUOTE]

This is turning into the quagmire that I expected to exist, before I fell into it.

It is the action of falling that explains the trapdoor, because there seemed to be nothing suspicious about proceeding from point A to point B. However, if I am told that there is one trapdoor which may be encountered during the movement between point A to point B, being located at point C, the trapdoor may as well not exist, because I will avoid it by not traveling toward point B via point C. Or I will test each potential step before making it.

I do not know however what it takes to trigger the trapdoor at point C, that not being given. If I know the trigger but not the location, I still will not fall through it, especially at point C.

So if one does not mind me saying so, the above logic may not be relevant as an explanation, but at least I value the sharing of it with me.

Probably everything in the world must be subject to one's perception of it, and what one does with that, that of course being a reasonable assumption.

Just because I am dealing with an equation, does not mean a supposed refutation of it by saying " 1 = 2 " or " 2 = 1 ". That is incorrect, even in my understanding of mathematics.

So by me asserting the ZERO = INFINITY may just mean that I have looked at that equation with a little more scrutiny, which I have chosen not to share with someone else yet. And believe it or not, my IQ being < 50 has nothing to do with my scrutiny; it's just a reflection, perhaps, of what one sees when one looks directly, tangentially, into the surface of a mirror, and wonders about the IQ of the person seen there.

I do next want to talk about Cantor and " Aleph 0 " but I will clear this thread of my presence first !

As for Leveque, I'll give you a hint: It's before about page 17, in his book about "elementary theory of numbers".....he spends about a half-page, discussing homomorphisms and isomorphisms, just after he defines a group, a ring, and a field.

And R* (R with the addition of infinity) isn't quite a group under multiplication, since infinity * zero is no better defined than it is anywhere else and therefore the set is not closed under multiplication; you have to take limits to get meaningful answers. (See "disproving boundedness of crank score" thread for an example of failure to appreciate that point)

Be *very* careful crossing the street -- remember everything is a projection, and some projections are deadly.

[QUOTE=R.D. Silverman;275463]Total horsesh*t. This is gibberish.[/QUOTE]

Next question: How close are (or aren't) we to showing that odd perfect numbers don't exist? Or is all that factoring just raising the lower bounds?

[QUOTE=Christenson;275633]Next question: How close are (or aren't) we to showing that odd perfect numbers don't exist? Or is all that factoring just raising the lower bounds?[/QUOTE]

The first question is meaningless. There is no way to measure "how far
away" we are from any unproven conjecture. There is no metric.
A proof may require just one little small idea beyond what we have
now, or it may require totally new ideas. There is no way to know or
measure the gap.

The factoring just raises the bound. It's been raised to 10^1500.
What they hope to accomplish by raising it further eludes me. It does
not aid in a proof. 10^1500 is just as far from oo as 10.

[QUOTE]What they hope to accomplish by raising it further eludes me.[/QUOTE]We've said it before, but we might as well say it again. We hope to get some intuition on the problem.

[QUOTE]10^1500 is just as far from oo as 10.[/QUOTE]But 10^1500 is not just as far from 0 as 10 is.

------

On the topic of the thread, if you define something so that it is inconsistent then of course it will equal anything else.

Is perfection a state or a process? If it is a process, then those who are perfect (i.e. working towards betterment) must simultaneously be imperfect (because progress is happening).

[QUOTE=R.D. Silverman;275711]The first question is meaningless. There is no way to measure "how far
away" we are from any unproven conjecture. There is no metric.
A proof may require just one little small idea beyond what we have
now, or it may require totally new ideas. There is no way to know or
measure the gap.

The factoring just raises the bound. It's been raised to 10^1500.
What they hope to accomplish by raising it further eludes me. It does
not aid in a proof. 10^1500 is just as far from oo as 10.[/QUOTE]

The first question isn't completely meaningless...it is pretty clear, that when Andrew Wiles went to work on FLT in dead earnest, that he knew he was close to proving Fermat's last theorem -- he could state the missing piece, and he thought he could provide it, eventually. [It's also math folklore that it was stated the theorem might be proved by combining the french and german schools of thought on the subject] It should also be clear to you from my question that followed that I knew the answer might not be known.

[QUOTE=Zeta-Flux;275713]We've said it before, but we might as well say it again. We hope to get some intuition on the problem.

But 10^1500 is not just as far from 0 as 10 is.

------

On the topic of the thread, if you define something so that it is inconsistent then of course it will equal anything else.

Is perfection a state or a process? If it is a process, then those who are perfect (i.e. working towards betterment) must simultaneously be imperfect (because progress is happening).[/QUOTE]

By way of no apology, I posted IMPERFECT = PERFECT and ZERO = INFINITY ( " tongue in cheek " ) to get the expected rise out of RD S. He is so predictable with his responses !

I also use the experience to measure the thickness of my skin or hide. He still got to me; must continue working on that !

Simon

Don't forget to give me your poll responses; I'll expect some changes after admitting to this. Also the way its listed give the expressions different meanings, especially if I am talking about a process rather than an object.

[QUOTE=9021951;275741]Don't forget to give me your poll responses; I'll expect some changes after admitting to this. Also the way its listed give the expressions different meanings, especially if I am talking about a process rather than an object.[/QUOTE]

you do realize it says anyone can view it so you can as well right ?