Mathematics

Hi all, Why say that the following phrase is nonsense? “The consistency of axioms cannot be proved within their own system.” Because: A system which has axioms for itself, in order for the system to call them axioms for itself, the system has to have a consistent behavior around those axioms and so when it behaves inconsistently with regard to those axioms, the inconsistency between those axioms and the system’s behavior the system can prove to itself. If what is written above is false, then when a system behaves inconsistently with regard to some axioms it has for itself, that inconsistency it cannot prove to itself, and it keeps behaving inconsis…

Following on from the "how many sides does a sphere have?" thread, I thought it might be interesting to see how people react when asked to describe Klein Bottles. How many (a) sides, (b) surfaces, © edges, (d) contained volumes do they have?

I'm doing my thesis now about Knowledge Management (KM) readiness assessment in organization. I'm thinking to use fuzzy logic for doing the statistic, and my lecturer advised me to use Fuzzy Multi-Criteria Decision Making (FMCDM). By the way, my research steps are: arrange the questionnaire using Likert scale, then weighted it using FMCDM method. But even I've read many many papers about FMCDM, I still couldn't find and still stuck about how to weight the scaled questions using this method? I hope you all can help me to solve my problems.

Link : deleted

So I'm doing this science fair project & its due SOON. Its about the genotype (the gene make-up basically) of red hair. I'm trying to come up with all the possible combinations of the genes, but I can't figure out the right equation/formula. Here's the deal: There are 8 alleles for hair color. HHHHHHHH or hhhhhhhh or Hhhhhhhh or hHhhhhhhh or HHHHHHhH, etc. How do I find the # of combinations???

Hey all, I was wondering, if one were to define a number r, for which [math]|r|=-1[/math], would it be possible to logically deduce it's behavior in mathematical operations? I know that the very concept is unimaginable and I also know it would be useless. But if we can have square roots of negative numbers, why not numbers denoting negative length? I'd be interested to know what [math]r^r[/math] would be, for example. Cheers, Gabe

Nope, not another boring, theological quest to find the value of 0/0, but in fact to disprove its existence... The simple proof that 0/0 doesn't equal any positive, negative, or imaginary number, then for example: 0/0=1, then 0/0(2)=1(2), making 1=2, if 0/0=2, we substitute 1 for 0/0. Now 0/0=0, this doesn't hold, so 0/0 might as well equal 0, nobody knows. This can be proven to not be able to be disproven by: a = b a^2 = b^2 a^2 - b^2 = ab - b^2 (a+b)(a-b) = b(a-b) a+b=b b+b=b 2b=b 2=1; This would be true that 0/0 cannot equal 0, but on line 5, a+b=b, we can subtract each side to get that a=0, in which case nothing can be proven for 2=1 …

saw this very interesting video: and wanted to share/talk about it in a place without 500 character limit lol i personally believe the answer can be considered undetermined, or both 0 and 1. to have a definite answer, we gotta know the number of 1's we have, and the operation sign we start with. starting with a - sign and having odd number of 1's means you have the final answer = 1 (1 - 1 + 1 = 1) and having even number of 1's means you have final answer = 0 (1 - 1 + 1 - 1 = 0). infinite, by oxford's definition means "impossible to measure or calculate" which means there is an undetermined numbers of 1's involved. to want an definite answer is to collapse th…

i was wondering if somebody had any ideas about this: the gradient of a horizontal line = 0 the gradient of a vertical line = infinity but the product of the gradients of perpendicular lines is -1 so does that mean that 0 x infinity = -1 ??? ... or is there something in the proof for the product of the gradients equalling -1 which excludes it for these values?

Can you explain how? how can 0!=1 and 1!=1 Thanx

I know this a topic which has been discussed to infinity, but I have a problem with this theory and would like other peoples' opinion on it. The 'proof' states that: x = 0.9999 10x = 9.9999 9x = 9 x = 1 I believe the problem lies in the second line already. Is it possible to do an arithmetic operation on a number with an infinitely repeating fraction? Let's take a finite number. x = 0.9999, then 10x = 9.9990. We have to know there are 4 digits after the decimal point, so each one moves one to the left, and the fourth digit after the decimal is replaced by a 0. I suppose the argument is with regard to the theoritical interpretation, but in practice i…

ever since we started learning division God knows when, i have been told that 0/1 cannot be done. but WHY? if we divide nothing by 1, wouldn't it just be nothing? but if we divided it by 2, wouldn't we have a lack of nothing? which is to say we'd have something? and if we divided 0 by 0, would we get infinity?

Okay, I just woke up and have had only one cup of coffee so far this morning, so I'm not quite awake yet. When I'm in this sleepy-time condition I tend to wander aimlessly through the internet. This morning I found myself looking at a youtube clip claiming that 0+0=1. And all of the comments on that page were having a grand old time bashing the poster of this clip. (I clicked out of youtube and now I can't find the clip again.) Anyway, while having my first smoke outside, my mind began to wonder how and why 0+0=1 could come even close to being a true statement. What I came up with is probably laughable, but could you kind people of a higher intelligence than mine (an…

If 50÷1 is 50 so 1 fits 50 times so I need to ask you how many times does 0 fit in 0 0 times right? So 0÷0=0?

06:12, 06:16 06:12 1 The root digit; a point or a circle, not a duet. Black standard hover. 2 The fount. Opposite, and polar the line. 3 The minor triangular. Wit, a tutor of the second a quiver. 4 Major, or the square: a fix, a gradient a scale. Skeleton. 5 Minute integer; agent of a quartet. A note on a blank canvas a pin 6 Naught. screw. 7 The enigma; corrival for the root digit. Sinister asylum, the lens. 8 Eclipse number. Opulent mien a lever. 9 Bone immaturity. The phobia, temper; a nexus. 10 The flux, a cross of hue and tint, multiplied. The perfect blend; the fly. 06:16 2 (8) Band (.2). 3 (9) Bezel (.5). 1 (10) Lug (.1).

Begin with Euler's Identity: [math]e^{i\pi} + 1 = 0 [/math] [math]e^{i\pi} = -1 [/math] [math]e^{i 2\pi } = 1[/math] [math]e^{i 2\pi} = e^0[/math] [math]i 2\pi = 0[/math] [math]i = 0[/math] [math]1 = 0[/math] Euler says so!

1^∞ ≠ 1? What, Is this really indeterminate? 1 * 1 * ... * 1 = 1 1 * 1 = 1 = a a * 1 = 1 = a edit: I misunderstood "indeterminate"

I know it is a no solution problem, but I was taking a look at it through the use of a limit and wanted to see whether this approach was valid. Given that [math]\lim_{n\rightarrow \infty }\frac{x+1}{x}[/math]. We can apply this to 1^x = 2, which can be turned into [math]log_{1}(2) = x[/math]. [math]x = \frac{log(2)}{log(1)}[/math] Now, this is undefined. Therefore, we can take the limit by applying the above together. [math]x = \lim_{n\rightarrow \infty }\frac{log(2)}{log(\frac{n+1}{n})}[/math] [math]x = \infty[/math] Is this math wrong? I am assuming some of it is, though checked wolfram: http://www.wolframalpha.com/input/?i=limit+of+x+approac…

I don't know how to ask this question, so I'll just give something; my question: is there a formula which can put this 'phenomenon' in a general form? [math]1^2 = 1[/math] [math]11^2 = 121 \rightarrow 1+2+1=4=2^2[/math] [math]111^2=12321\rightarrow 1+2+3+2+1=9=3^2[/math] [math]1,111^2=1234321\rightarrow 1+2+3+4+3+2+1=16=4^2[/math] [math]\cdots[/math] How can this be put in a general, mathematically more plausible expression? I think that this is a 'crucial' part of it: (I found it about a few minutes ago; sorry if it's wrong, haven't seen summations in school yet..) (To be honest, I'm pretty happy with the result that I found this ^^ ) [math]\left[\sum…

Picture this, you have an array of 1,000,000 light bulbs, numbered 1 to 1,000,000, all of which are off (and all of which work). The following task involves these light bulbs and an action we'll call "flipping". Flipping simply means changing the state of a light bulb. If the bulb is off, flipping will turn it on. If the bulb is on, flipping it will turn it off. Starting with all the light bulbs off, you start at bulb #1, and flip the state of every bulb. Once you've done that, you go back and start with bulb #2, flipping the state of every second bulb. Next, you go back, start with bulb #3, and flip the state of every third bulb. This continues all the way up…

Could anyone walk me through on this equation and what proves its validity?

1/(1/0)=? (not limit) Is it zero or undetermined?

It can be shown that as x approaches 0 from the right side, 1/x will approach 1/0 and apporach positive infinity. And it can be shown that as -x approaches 0 from the left side, -1/x will approach negative infinity and apporach -1/0, which is equal to (-1/-1)*-1/0 equals 1/0, since 0 is neither positive or negative. Showing that 1/0 is not even a number, and does not represent a distinct point on the real number line.

Hi all again! I'm sure there is a simple answer/solution to this problem...or a way to do it anyway, i just can't seem to get it. why does this = 1/e? Thanks Sarah

Addition is an axiom of mathematics, or am I wrong? I heard that the Peano Axioms can prove 1+1=2, but I don't really know why or how. Can any of you more advanced students dechiper this? (I'm only a freshman in high school, remember, and it's frustrating to not be educated higher in math.) So, if anyone can relate this to me, I'd be grateful.