i saw an equation in my dreams lastnight! opinions?

[LegionOnomaMoi]

That's the right one. instead of .3333.... Use the series for .99999 set x=Sn and pull out number the first number from the series after you multiply by 10. Then you can take away x without violating order of operations. To get .9999=1 if infinity=infinity-1(which it does). And voila 1=.9999....

I'm not sure I want to do that (it work, of course) because I want to retain the original .333... for continuity (that is, the structure of the 3*1/3 with 1/3 being represented by the series that converges to that point). But as is I do need to put the constant 3 in a different place so that it is multiplied by each term. I think I might like using convergence better and pretending (again, for continuity) that the sequence takes the place of the infinite decimal.
This is basic stuff. I'm wondering how much I'm forgetting because I haven't worked in analysis (well, data analysis all the time but it's quite different) and how much is due to sleep or something else but I feel like there are things on the tip of my brain that are bugging me still. This is annoying. I feel like I want to use cuts but they won't preserve the .3333... part any better than the much easier method of using the series for .999... and ignoring putting the constant 3 in so that it sums with each term s.t. as n approaches infinity we get 1. And continued fraction representation isn't any better.

 

[lewisnotmiller]

That's the right one. instead of .3333.... Use the series for .99999 set x=Sn and pull out number the first number from the series after you multiply by 10. Then you can take away x without violating order of operations. To get .9999=1 if infinity=infinity-1(which it does). And voila 1=.9999....

I always think of it as what is added to .99999 (repeated) to make it 1?

.0000(repeated)1?

 

[LegionOnomaMoi]

I always think of it as what is added to .99999 (repeated) to make it 1?

Without getting into the epsilon form of the proof, the ability to show we can make .9999... as close to 1 as we please.

 

[ladybug77]

I know what it is now.
Is love the exact opposite of fear, or hate?
Or is it possible love is equal than OR greater to fear, or hate?
How do you measure love?
How do you proove we love each other??
Or is love really nothing??

 

[ladybug77]

If we cant measure love, is it possible that love is really all we possess??

 

[ladybug77]

So what is really worth measuring?? What is my own personal worth??
How do i measure myself? And how will God measure my worthiness??
Based on how much love i possess is the answer.

How do i know i possess love?

Because you can loose everything else that can be measured.

Its called possessing the holy spirit.

 

[ladybug77]

So what is really worth measuring?? What is my own personal worth??
How do i measure myself? And how will God measure my worthiness??
Based on how much love i possess is the answer.

How do i know i possess love?

Because you can loose everything else that can be measured.

Its called possessing the holy spirit.

And i would rather die than anyone take that right from me.

You can rewrite and edit the constitution. You can strip all rights away from me.
You can steal all my money. Take it, if you think you deserve it! Take my car, my house, my food! For crying outload! America is starving people! I havent eaten for a day and a half! My work is not measured by joules!! Its measured by time!! No matter how hard they work me...no matter how much energy i put out. Im payed by time! Fair?? No! But i dont mind that much. Its still a tiny tiny amount of paper used to trade items!

There is one infinite thing that NO ONE can TAKE from me! Even if only infinite until death on earth!
My own self-worth!! And I AM the strongest one girl army that could ever be.
Because i love the ones who have stripped my freedoms!! For now...i see what i lost.
And i see all i have left.
How ironic.

 

[crossfire]

So what is really worth measuring?? What is my own personal worth??
How do i measure myself? And how will God measure my worthiness??
Based on how much love i possess is the answer.

How do i know i possess love?

Because you can loose everything else that can be measured.

Its called possessing the holy spirit.

In Buddhism there are the Four Immeasurables:

1) loving-kindness or benevolence (metta)
2) compassion (karuna)
3) empathetic joy (mudita)
4) equanimity (upekkha)


Brahmavihara - Wikipedia, the free encyclopedia

 

[LegionOnomaMoi]

Without getting into the epsilon form of the proof, the ability to show we can make .9999... as close to 1 as we please.

Perhaps it's the meds and sleeplessness talking, but these proofs are so essential to mathematics it might be worth going over some when I have a functional brain. Granted, I suck at simplifying but as long as this thread is about numbers and mathematics it couldn't hurt to examine some of the higher-level basics if that makes any sense

 

[Revoltingest]

Without getting into the epsilon form of the proof, the ability to show we can make .9999... as close to 1 as we please.

What!? You say "as close...as we please."!
.9999... is exactly 1! (And no, that is not 1 factorial.)
You know the easy proof, bub!
I'm deeply offended at your.....oh....wrong thread....I thought I was in...never mind.

 

[LegionOnomaMoi]

What!? You say "as close...as we please."!

I do. It's the informal version of the definition of limits of convergent sequences. If you'd like to render that definition in better plain English than I, I beg you to. I end up saying things like "remember the definition of a limit in single variable calculus? Well..." and too often they don't remember and if they did my explanation makes them unsure of that and doesn't teach them what the new limit definition entails. But the main point is it is equal only through a limit definition as we can't symbolically represent infinitely many terms.

I'm deeply offended at your...mind.

You hate my mind! How DARE you express such sentiments in a blatant misquote I gave of you!

 

[4consideration]

I know what it is now.
Is love the exact opposite of fear, or hate?

I do not think so. I think it depends on how one defines love, though. If one uses a definition that love is only an emotion, then it would make sense to see it as an extreme, polar opposition, of a feel good emotion.

Or is it possible love is equal than OR greater to fear, or hate?

I think of it more like: that love is a quality of being, an orientation point (where one is viewing the situation, or coming from) and also a power.

How do you measure love?

I think that one has to first reduce love (or look only at a specific aspect of it) in order to measure it. I think it is usually best not to try to measure it, because of how much one leaves out in the process.

If one reduces love to an emotion, then love is only what feels good. And...something that may actually feel good, but be harmful in the long run, can easily be confused with love.

How do you proove we love each other??

I think behavior is often an indicator, but not "proof". IMO, actions motived by ego, or personal agendas (like looking good) can easily be mistaken for love if love is viewed only as an action or an emotion. I think the real proof is in the intention behind the action, which I don't know how one may prove or demonstrate conclusively.

Or is love really nothing??

Nothing is something.

I think there is what I refer to a divine paradox in the way love often operates.

Most of what we are accustomed to dealing with in daily life operates by certain rules. If you have a pie and a few people, and then more people come in to share in it, the piece for each gets smaller in order for all share it equally. But...I think...an idea, and also love, expands according to how many share it. It grows.

This is often overlooked, I think, because if we think of things like "time" and "attention" as setting the standard for "how much love we get" that is divided, just like the pie. There is only so much time in a day.

But, if we look at love in the same way we may think of an idea...there is always enough for everyone, because there are no limitations, except those that we artificially insert. Within that concept of love being without limits (unconditional, not relying upon any certain set of conditions in order to be what it is,) there are ALSO relationships that may be formed. Relationships do usually have some kinds of established boundaries, which set conditions on the relationship.

For example, the love relationship between two people, in a sexually exclusive relationship, has established boundaries so that certain expressions of love are reserved for that relationship.

Love, as a whole, does not need to be limited, only a certain type of expression of it. I think sometimes people get insecure about love as a result of first having reduced it to something very small, like an action or emotion -- so that there may be a prevalent tendency of ideas like: don't love them too much, or else that must mean you don't love me as much.

I think love is one of the biggest subject there is -- a quality of infinity, perhaps.

 

[Ouroboros]

Hehehe. I have never come across that one before. It's very cute. I like how 3/3 is "broken" into (3)*(1/3) and how (1/3) is "decimalized". If you have more, please do share.

Or maybe "decimated".

 

[Ouroboros]

Never post on elementary math at 1 in the morning.

LOL! I saw your other post and I was like ... wha'?

3*1/3 and 3 * .33333 are not the same statements.

Agree. And I actually do know and understand why my little puzzle goes wrong, but hey!, what's the fun in giving it away?

 

[Ouroboros]

There's also series notation:
Let

where
Sn= 3(10^-1) + 3(10^-2) + 3(10^-3) + 3(10^-4) +...+3(10^-n)

Now it should be that

That's probably wrong but if so I'll fix it when I wake up.

I don't think it's wrong, but I could be wrong also.

Intuitively I understand what goes wrong in the puzzle, but I can't represent it well in math. What you wrote there is very close what I was thinking. Bring in the 3 into the lim and simplify (I think... without trying it... just shooting my opinions from the hip).

Another one would be to rewrite 1/3 as a ∑. 3*∑, bring in the 3, simplify, etc.

Yet another one, which I'm not sure how it would be done, might be to somehow rewrite it as a lim(f(x)/g(x)) and see if we can get to a condition and use L'Hospitals? Maybe... just spinning my wheels here.

I feel great though... I managed to get some of the brilliant minds on this forum engaged in a silly puzzle. LOL!!! (Great reading all your posts btw)

 

[crossfire]

I know what it is now.
Is love the exact opposite of fear, or hate?
Or is it possible love is equal than OR greater to fear, or hate?
How do you measure love?
How do you proove we love each other??
Or is love really nothing??

The immeasurables are considered to be a cure for many of the mind-poisons like greed, hate, and delusion. Some of your words here echo some of the words in this short excerpt from the Metta (loving kindness) Sutta, which I think you might enjoy right now.

Mettam Sutta: The Brahma-viharas

 

[Poeticus]

bump..

 

[LegionOnomaMoi]

I don't think it's wrong, but I could be wrong also.

I forgot about this. I'll look over what I wrote later to see where and in how many places I went wrong. In any event, we don't really need limits directly:

The absolute value of the ratio between terms means not only do we have convergence but a specific formula. It isn't as close to the original structure as I want, but at least we retain the multiple 3 and although it is multiplied by a complex fraction, at least the expression itself comes from a the series summation so the formula that replaces the simple fraction 1/3 in the final equation is directly related to the infinite sequence of decimals in a way that wasn't so before. Or not. It's not what I wanted but it's serve until I bother to do what I wanted to do yesterday.

Intuitively I understand what goes wrong in the puzzle, but I can't represent it well in math.

Yeah I get that a lot with particular types of problems, usually when I am doing a lot of boring calculations (sometimes it's worse if they're easier, actually) that represent the legwork in getting a solution to a problem of a type I don't work on a lot either teaching or for work. This happens even for a few problems types that I do cover with students somewhat regularly. For example, no matter how many times I do it, every single time I'm demonstrating approximating area with Riemann sums I'll screw up the notation at one point and sit there, being watched by people who until amount ago thought I knew what I was talking about, trying to figure out where I made what mistake this time. I think it's psychological- I hate teaching a few topics in calculus as they are presented in most of the textbooks I have to teach from because I think the entire approach is wrong.

The other big problem is that for work I have MATLAB and R. One of the biggest pains that is related to any number of applications in all kinds of fields is doing things like matrix manipulation by hand (whether it's simple multiplication or finding the characteristic equation or even just row reducing). I got used to it when I had to learn, but it's been a long time since then and now I almost never have to do the actual computations. Most of the actual matrices used involve too many computations to do by hand anyway. Every once in a while, though, I'll need to do some computation by hand and even when I'm alone I get embarrassed. The computations are easy it's just that I loose track of this number, put that one in the wrong place, or accidently add rather than subtract, etc. Then when I realize I messed up and go back, I get lost. The calculations are so boring I can't have trouble not focusing and rushing through them while thinking about the problem itself. As a result, tracing what I was doing just a few minutes ago to pick up before the error or even find it is a challenge. It's not just that I scribble, I don't write down all of the things I should and what I do write I just scribble haphazardly wherever there is room. Someone looking that the scrap work would have trouble figuring out if I was working on 1 problem or 14 different ones. It's extremely bad form and mathematicians the world over would have me tarred and feathered if they knew.

What you wrote there is very close what I was thinking. Bring in the 3 into the lim and simplify (I think... without trying it... just shooting my opinions from the hip).

I think I had the same thought myself and then I thought that moving the 3 either makes it a part of the summation which doesn't work or it's a constant which means pulling it out is the same thing. But I was happier with the seed of an idea in the post before my last one anyway, for the simple reason that it is more interesting. Alas, although I did remember this post earlier I got distracted.

I always loved but never practiced enough of real or complex analysis, and a lot of what I did was disjoint (e.g., rather than actually plow completely through the necessary material I'd go over it in pieces from time to time or come across a topic analysis shares with something more relevant to work or a different hobby like fields). I know there are more ways, or at least more nuances and intricacies to the way I know, to construct the reals. I had wanted to go in that direction and use cuts or something. I am also somehow oddly obsessed with preserve as much structure to the original expression 3*.33333... as is possible but complete with a proof that the representation I use just look more like that expression than some but also is, well, clearly justified. I think one of the reasons I like proofs so much is because it is the only form of expression I am capable of that, whether right or wrong, contains at most only a few extraneous steps and all the steps are written clearly and concisely.

 

[PolyHedral]

I forgot about this. I'll look over what I wrote later to see where and in how many places I went wrong. In any event, we don't really need limits directly:

Where did you get the (3/10)/(1-1/10) from?

 

[Ouroboros]

It's cool that it's possible to write math formulas this way. I didn't know about codecogs before.

I'm not going to add anything to your in depth analysis of this puzzle.

Yeah I get that a lot with particular types of problems, usually when I am doing a lot of boring calculations (sometimes it's worse if they're easier, actually) that represent the legwork in getting a solution to a problem of a type I don't work on a lot either teaching or for work. This happens even for a few problems types that I do cover with students somewhat regularly. For example, no matter how many times I do it, every single time I'm demonstrating approximating area with Riemann sums I'll screw up the notation at one point and sit there, being watched by people who until amount ago thought I knew what I was talking about, trying to figure out where I made what mistake this time. I think it's psychological- I hate teaching a few topics in calculus as they are presented in most of the textbooks I have to teach from because I think the entire approach is wrong.

I only know one or two textbooks. I took some calculus classes a few years ago (I'm old, so most of what I learned drained from my brain quite quickly, hence my inability to produce those eloquent formulas you presented above ), and the textbook we had sucked... big time sucked. Teacher's instructions were clear and comprehensible. Textbook... I couldn't read it even after I understood what it was supposed to teach. Yuck!

The other big problem is that for work I have MATLAB and R. One of the biggest pains that is related to any number of applications in all kinds of fields is doing things like matrix manipulation by hand (whether it's simple multiplication or finding the characteristic equation or even just row reducing).

Eeek! Matrix by hand!!! Don't get me started! It's like stabbing a fork in your knee and then run a marathon.

I got used to it when I had to learn, but it's been a long time since then and now I almost never have to do the actual computations. Most of the actual matrices used involve too many computations to do by hand anyway. Every once in a while, though, I'll need to do some computation by hand and even when I'm alone I get embarrassed. The computations are easy it's just that I loose track of this number, put that one in the wrong place, or accidently add rather than subtract, etc. Then when I realize I messed up and go back, I get lost.

Oh, I so know the feeling. And the error is usually something extremely stupid like one simple missed negative sign. The worst error I kept doing unintentionally was computing 3*3 as 27 and 3^3 to 9... DOH! Now I know at least to watch out for that particular mistake since my brain insisted on the faulty calculation when I was in a hurry.

The calculations are so boring I can't have trouble not focusing and rushing through them while thinking about the problem itself. As a result, tracing what I was doing just a few minutes ago to pick up before the error or even find it is a challenge. It's not just that I scribble, I don't write down all of the things I should and what I do write I just scribble haphazardly wherever there is room. Someone looking that the scrap work would have trouble figuring out if I was working on 1 problem or 14 different ones. It's extremely bad form and mathematicians the world over would have me tarred and feathered if they knew.

Sounds like you're a math guy with ADD.

Well, there are all kinds of math teachers/guys/gals. The most interesting teacher I had she was in her early 60's. She was a control freak. A math genius of a kind I've never met before. She had a watch set to beep at certain intervals in class to remind her of switching to next item on the list. The worst part was to try to write down what she wrote on the board. She wrote, calculated, and foresaw where everything was going faster than we could copy it down. She was done when we just started. She was very impressive.

I always loved but never practiced enough of real or complex analysis, and a lot of what I did was disjoint (e.g., rather than actually plow completely through the necessary material I'd go over it in pieces from time to time or come across a topic analysis shares with something more relevant to work or a different hobby like fields). I know there are more ways, or at least more nuances and intricacies to the way I know, to construct the reals. I had wanted to go in that direction and use cuts or something. I am also somehow oddly obsessed with preserve as much structure to the original expression 3*.33333... as is possible but complete with a proof that the representation I use just look more like that expression than some but also is, well, clearly justified. I think one of the reasons I like proofs so much is because it is the only form of expression I am capable of that, whether right or wrong, contains at most only a few extraneous steps and all the steps are written clearly and concisely.

Sure. I'm not going to argue that.