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Sorry, I'm here, I'm just trying to figure the huge text out, I haven't done it before, but my next post should be in larger text, sorry for the wait...
Yes, I'm here, sorry, was trying to read through the post. No, I'm actually self learning. From reading though, it seems you had a few problems in school, I can definitely relate to that...unfortunately. As for what I'm learning, I'm still trying to learn calculus, but I often...review things (like from algebra), to make sure I have a good grasp and understanding of them. Um...I noticed bob bundy was talking in huge letters, did you want me to do the same?
Hi, okay, yes, I can talk on you page. Um...I can also help you with whatever I know, but I am currently in the process of learning myself, so I might not be as...knowledgeable as some of the other members I've seen. But either way, I will help anyone who asks if I can.
Well, long story short (I don't know if you read before hand), Sarah Rebekah 16 didn't want to live anymore and was asking for help. But now it seems that she is better. For more details, it would probably be easier just to quickly read through the topic...
Hmm...? I'm a little bit confused, what do you mean send messages? Like PM through the forum? Post on a specific topic? What is your page? (sorry, I'm honestly unsure what you mean by all of that)
Unless I'm mistaken, it's more then simply for convenience. Also, 0.¯9 doesn't end, because the ¯ over any number (which I put before the repeating number because otherwise I'd have to show in a picture), means it goes on forever. If it had an end, that means we'd be able to put something after it, therefore, there'd be no reason for this controversy in the first place.
Um...if calligraphy is me, I live in Pennsylvania...so I'm in the eastern part of United States, GMT - 5:00. That the reason you wanted to know?
US? I live in the US, and still, it's tomorrow. Within the US isn't a whole day time difference last time I checked. How long was a long time ago (asking out of curiosity, because I really don't know)?
Hmm, I was just thinking, is this related to that 2012 end of the world stuff at all (as in yet ANOTHER way the world will end in 2012)? On top of that, I think I noticed an error...
The article is apparently dated January 26, 2012, but...
Sources confirmed that if a death solution is not in place by Mar. 31, the U.N., in the interest of preserving the human race, will mobilize its peacekeeping forces and gun down as many people as necessary.
It is past March 31st...and I haven't heard anything about U.N. gunning down anyone in the interest of preserving the human race. Did they mean march 31'st of 2013? 2014? 5000? Because unless I'm mistaken, it sounded like they were talking about 2012... Unless they meant 2025 like when they mention here (though later in the article)...
"I don't care how it happens, but a ton of Africans have to go, because by 2025, there's no way that continent will be able to feed itself," said Dr. Henry Craig of the Population Research Institute.
But that specifically says the Africans, and this article also made it seem like we were in immediate danger. However, that suggests that it's even later for the rest of the world, doesn't it? I don't know, I'm more questioning the validity of this article, as in, just how correct their information really is...
How is that less torture to the people? I mean, with the sun, it would be more or less quick depending on how fast we were going into it, but a black hole, I wouldn't even know where to begin with that. Just to start you'd be stretched further and further the closer you get to the black hole (and you wouldn't even be in the black hole yet), let alone all of other stuff that would is theorized to happen to you. I don't know, I don't quite agree a black hole would be less torturous...
Hmm, wow, I was not expecting that.
I am personally rather curious about the facts of this, as this seems to be a rather...opinionated article. I remember being told before, that as we grow in numbers, we increase our resources to survive on as well (not quite that simply though). I've always had...arguments about that to say the least, but that shouldn't mean what they are suggesting. I've realized our world population is... well very large, as I remember learning about. Such as if you track our population from 0 ad to what it is now, the only time the overall population has ever decreased was from the black plague. Even wars like WWII did not decrease the world's overall population from growing. But still, I'd also love to see how they decide to do this, because I'm very sure at least 1/3 of the world's population is just going to kill themselves so the other 2/3s can live on happily (being sarcastic)! However, it personally worries me too, supposing there is truth to this that is. Again, I would like to see the facts behind this reason. Also, the solution they give is ridiculous, surely there are much better ways of handling it.
Hmm, I guess it's different for everyone else. Where I live, Thanksgiving is tomorrow, regardless though...
Happy Thanksgiving everyone!
Glad to hear you are doing better, and I hope it lasts too! However, my same offer still stands if you want someone else to talk to.
Well, I guess I can try to be a little bit more clear...
Calligar wrote:I myself do not...personally believe this as a mathematical "fact," but also realize how futile it is to argue against it. So like those many, it is impossible to convince me as well, after all, there is a reason this idea is so highly controversial.
The term mathematical fact might be a little vague. First, not every number is rational -- not every number can be represented as the quotient of integers. For example the width of a square whose area is 2 is not a rational number. That is, we need the full blown set of real numbers. Figuring out what the real numbers (really) look like is a hard challenge, and providing a description of them in set theory was a major challenge. There are two main approaches: Dedekind's cuts and Cauchy sequences. They produce the same set. Essentially, take a bounded sequence of rational numbers, and identify a "number" L with this sequence. The real numbers are the rational numbers with all these Ls. Thus in the construction of real numbers, we see that every real number is the limit of a sequence of rationals.
In other words, the real number "1" is by definition the limit of the sequence
<0,9,0.99,0.999,0.9999,etc
Firstly, when I say mathematical fact, I am really just referring to what is currently accepted and arguably "known" in mathematics. Secondly, the limit of sequence is just another way to represent it being infinitely close, but still not exactly equal to the number (unless I'm mistaken). Just like for it representing 1/3 with <0.3,0.33,0.333,etc. (I might not have put everything in proper terms, sorry if that causes any confusion, wasn't sure how to say it simply off the top of my head). Also would like to make a note, you messed up slightly when you posted; it should be 0.9, not 0,9 for the first one unless I'm mistaken (but doesn't really have any relevance to anything). In other words, it is just more rules that exist that otherwise, as I was saying, prove it's a mathematically fact. Remember when I said this...
To be fair, the proofs they offer can be argued from a logical standpoint (so long as you understand everything that is going on), but there is nothing in mathematics that can prove how they are different otherwise.
In mathematics, there is no way to represent the difference between 0.¯9 and 1. All proofs (including false ones) either assume things (for specifically this), or simply define it as one only because of the infinitely close distance (there might be a few other reasons, but those are the 2 major I see). Even though some people will argue things like it is 0.0...1 away, or 1/10¯0 away, which might arguably seem right, one can argue about the infinite distance, therefore making it an impossible argument to win. So this argument doesn't carry on (with me) over confusion, I'll explain in more detail.
Rules in math already say this is true (even though it is very controversial) for many reasons. However, it largely also comes down to one major thing: saying that one number equals a number that isn't exactly the same. In other peoples eyes, that would be like saying 2 = 1; the only reason for it not being like this is because of the rules for it (plus all of math as we know it would collapse). Also, the whole reason for this controversy in the first place, is because of using decimals in a way that don't accurately represent what it is. Decimals can't accurately represent everything, unfortunately, no system can (at least that I know of). However, unfortunately in this case, things like hyper real numbers define this, which is where the controversy comes in (I am not saying hyper real numbers are a bad thing though). There are other similar cases of this. 1/3 = 0.¯3, right? But wait, there is a difference, isn't there (asking rhetorically)? Why? Because 1/3 can not be accurately represented in decimal form. Changing 1/3 into a decimal will give you 0.3...3...3...forever. However, there isn't that number at the "end" to...well end it. It is just like pi in that sense; pi = 3.14159265..., however there is no end to it. There is no way to accurate represent the number in decimal form, or in any form for that matter (that I know of), besides for just calling it pi. It is that very reason I've seen people argue pi ≈ 3.14159265...instead of =; because no matter how long the decimals go, it doesn't exactly equal pi because there is no end to it (rather pi is mathematically = or ≈ to 3.14159265... in this case is irrelevant to what I'm trying to say, plus I never said which one it is).
Please just keep in mind I'm not exactly arguing for or against. I'm trying to say overall that it is futile to argue. I might be personally against the current idea in math, but I have learned to accept that this is currently mathematical fact. I just wanted to make all that clear.
Hmm...this is not good. I can give my information if you still need some help and someone to talk to, but it seems mandy jane has already offered you their help. For your sake, I hope you don't go through with it, but I also don't know enough yet to even try to help you. Just in case though, just inform me if you need anyone else to talk to, after all, you now have everyone on here worried about you!
hi dvcochran,
welcome to the forum!
Hi zehao1000,
welcome to the forum!
Very impressive for a 12 year old! I also did not know this theory, it is definitely really interesting; I can definitely understand why mathematicians would be fascinated over it.
I personally wasn't a big fan of contests myself, not to mention I don't feel I was the most suitable back then. I was in one math contest in my life, I actually moved on to um...I think they called it regionals (where the best from the different schools of the region compete to see who's the best), as only 2 from our school were allowed to move on. In the regionals, only the best person moved on from there, and it wasn't me, but the other one from the my school. I was very...ignorant back then, and regret that I put forth no effort into learning, as I probably could have moved on even further than that if I at least tried. I honestly didn't even know anything about the contest I entered; my teacher was sharing it, I knew I was good at math, and figured it would be fun.
Though my own experience might have been more of a failure, if you love these contests, I encourage you to continue on. If your dream is to make it to that point in the contest, then I strongly encourage you to do so! I might not be very familiar with the contest you're interested in, but I'm pretty sure you have the potential. Though, I would personally like to caution you on "bragging" about your own abilities too (like to your friends and stuff). It can discourage those who otherwise would want to take up math later, even if you only joke around about it. On top of that, it can show your own incompetence.
Anyway, after this long post, I know the next contest isn't anytime soon, but I wish you luck in it anyway! Also, if you need help, there are plenty of mathematicians on this site that can help you.
Hi Sarah Rebekah 16,
welcome back to the forum!
Hi, princess snowwhite,
welcome to the forum!
This is a very good place to come, plus from my experience, very friendly as well. MIF seems to work a lot on the main site, as there is plenty to see. Almost everything is usually well done, and on the easier side to understand. Whatever you don't find there, you can most likely get help from people on the forum. If one person doesn't know, someone is bound to know and will respond. Hope you both learn and have a good experience with this website.
I'd agree, because I have high emphasis on myself for understanding things. It really bothers me if I walk away from something without understanding it well. It has also done nothing but help me with...well pretty much everything I know now (though there is still a lot I don't understand). So yeah, I will often question something I don't understand to better understand it.
Actually, I just realized I was looking at it differently. This in my opinion is another futile argument, I understand why it's a rule now. No need to further explain to me. I also understand the 2 = 1 proof now and see the error, I was having a...similar kind of issue with it. So with all my questions answered, I go back to with what I was originally going to say, but didn't say it quite clearly. I think the continuous functions page is very clear and well done. I didn't have an issue understanding it, only understanding indirectly relating things.
Wow, read that whole thing, but, can someone please explain to me the joke part, it just seemed like one big...interesting story (I'm usually slow at grasping jokes in the first place...)?
Okay, I understand the fact that you can not divide x by 0, but i was strictly talking about 0 / 0, not 1, 2, or any other number. I don't understand why you can't divide by 0 in that case, because I do see 0 x 0 = 0 if u changed it to multiplication. Also, I didn't realize that rule applied to 0 as well, that was why I was asking. I already knew about stuff like 1/0 is undefined though and already understand why that is. Also I have read every post, and it still doesn't seem to prove to me that 0 / 0 is undefined, maybe because I'm looking at it the wrong way? Though I also worry about arguing this further, as this might only end up being something just like 0.999...=1. So, I'm just going to assume its a rule right now I don't... personally agree with. If there's better reasoning for it though, I would not mind hearing it.
Nice! Anyway yeah, thank you.
If you are talking about the 3'rd line where it says, (a-b)(a+b) = b(a-b), you are multiplying, not dividing, unless I'm missing something...?
Also, I'm not sure I quite understand the reason for simplifying it. Everything seems fine about it too me...