Mathematics

Is 1+1 always 2? I tried to prove that 1+1 is not always 2 with applying Goedel's incompleteness theorem as; http://hecoaustralia.fortunecity.com/incompleteness/incomplete.htm

Gauss's law describes the electric field created by the point charge. This law is applied when the point charge is isotropic only. Do you think it's a trivial matter? I don't think so. I tried to extend Gauss's law to the case when the point charge is not isotropic in the following site; http://hecoaustralia.fortunecity.com/gauss/gauss.htm

When it comes to using relational operators on scalar values, there's usually no problem. But what about vectors? Are there any generally accepted rules or consensus when it comes to relational comparisons (ie. =, <>, >, <, >=, <=) of vectors? For instance, consider v1 < v2 for the two vectors v1 = (10, 8) and v2 = (5, 10)... Does one then compare the x and y values pairwise and return a boolean for each value, in this case (false, true)? Or does one check the magnitude of the vectors against each other and simply return (false)? Or something entirely different...? Cheers, Michael

Does anyone know what the steps are to get "h" at just one side of the "=" sign? It's an equation from a physics book whih I just can't work out how the answer h is arrived at. t1 = 0.69s & t2 = 2.37s g =9.81m/s h =(h+0.5gt1^2)/t1)t2 - (0.5gt2^2) The answer is h = 8.02m Many thanks G56

simple yes or no ramsey say the axiom of reducibility is he right or wrong russell wittgenstien and others say the axiom id invalid are they right or wrong Poncicare Russell and philosophers say impredicative statements are invalid are they right or wrong

(X¡ôN)¡ê(XX) Now take X to be N, and we have the contradiction (N¡ôN)¡ê(NN) Known of these was given by Russell himself in 1919 and concerns the plight of the barber of a certain village who has enunciated the principle that he shaves all those persons ans only those persons of the village who do not shave themselves. The paradoxical nature of this situation is realized when we try to answer the question, "Does the barber shave himself?" If he does shave himself, then he shouldn't according to his principle; if he doesn't shave himself, then he should according to his principle. Other attempts to solve the paradoxes of set theory look for the trouble …

given (3?3)?3?3?3=29 using + - / x only once

(Before you read this, you better read the former thread, in this forum, under the same tittle) Continuing the first thread, now I'll give you more tables that are filled with numbers only 1 to 40, so it won't much hurt your eyes. Thus many rows are blank. I put the file in .xls format at: http://www.artofproblemsolving.com/Forum/viewtopic.php?t=171338&sid=dbfa1e1099d59aa7b0714fb0b192b6e4 Tables 1-20 in sheet #1 & #2, are same as before and have been corrected some (of mistyping), Tables 21-32 in sheet #3, Tables 33-44 in sheet #4,...,Tables 273-284 in sheet #24, Table Total Amount in sheet #25. I name and arrange the tables just like that, though you can …

Complet text of the proof All wholes numbers in the next are given in the prime base [math]n[/math]. Here are the known positions, repeatedly discussed on the mathematical forums. Thus, let (1°) [math]A^n+B^n = C^n[/math], where prime [math]n > 2[/math] and [math]A, B, C[/math] have no common factors. Let for the moment the number [math]ABC[/math] is not divided by [math]n[/math]. Then: (2°) [math]C^n-B^n=(C-B)P[/math], where [math]C-B=a'^n, P=a''^n[/math], [math]C^n-A^n=(C-A)Q[/math], where [math]C-A=b'^n, Q=b''^n[/math], [math]A^n+B^n=(A+B)R[/math], where [math]A+B=c'^n, R=c''^n[/math], [this follows from the simple lemma: if the numbers […

How do I graph a parabolic equation on a graph? for example 2x^2-3?

I had a question in a recent exam that asked you to prove the formula to calculate the sum of an A.S. I only got 2/11 on it so i was wondering if someone could tell me it. I have searched the internet for one but all seem to be a bit rubbish and i think i can get better results here

HEY guys I am stumped could someone please tell me how long it takes light to travel 1 foot and 2 feet I know its in the millionths of a second but I cannot figure it out I must have the IQ of a penny thanks in advance...

Can someone please explain to me what complex numbers are?

For the following function, C computes the cost in millions of dollars of implementing a city recycling project when x percent of the citizens participate.C(x) = 1.5x divided by 100-x any one know how to solve this

Prove that the numbers 49, 4489, 444889, 44448889,..... obtained by inserting 48 into the middle of the preceding mumbers are squares of integers. Please give a formal mathematical proof involving Arithmetic progression or Geometric progression, not just verification.

I was playing around with my calculator trying to draw shapes on the graph and I have a question. As it enumerates through the various values, for say an equation that I graph, is there anyway after the fact of the equation to tackle any element in the list? I don’t have any real clue as to how to go about such or even if its possible. Does the graph just proceed and or execute from the opening argument with no ability to grab an element in the list after the fact. I mean in comp sci you have operators that can allow you such a luxury so I think they would exist in math. Would it be only possible by the constructing your initial equation or equations for that matter…

In the attached equation, is there any way to analytically solve for x?

I know that infinity is indefinite, and thus could be regarded as not being a number. With that, I realize that attempting to perform any arithmetic operations on infinity(other then 1/infinity, but that technically isn't an arithmetic operation either, though it looks like one) is both futile and meaningless. I thought that the limit of f(x)=x^(0.5) or (x+(x+4)^0.5)^0.5 is infinity as x approaches infinity. However, the graph of y= x^0.5 appears to have an horizontal asymptote (it does however, appear to be indefinite) Why is there such an asymptote? Is the square root of infinity some other indefinite constant which is not infinity? Or is the square root still infi…

How do I creat basic parabolas using this particular calculator?

What are these laws and how do they fit into mathematics? I am having trouble understanding them...

how do you solve pairs of simultaneous linear equations?

Take a diameter, for this case we use 9 inches. To find a linear plane of an arc we would multiply the diameter by 2. Now 18 inches. We would continue to multiply each diameter by 2 for 18 expressions. In the final 18th expression there will be a linear plane within the arc of the circle equal to three of the original 9 inches. Taking the diameter of the universe to be 18 billion light years, we use our formula in reverse, and divide by 2 for 18 expressions. This formula will continue for 9 expressions within the physical material universe, making 9 linear planes.

This is my online shopping list: Free graphing calculator (open source?) all the bells and whistles, capable of most anything mathematical. Online mathematics course, free. Brings you from intermediate to advanced, in most math forms. Finally got the time to learn! Thanks.

Rearange to find x in terms of y and t, in simplest form. (assume [math]y+3t\neq0[/math]) [math]y(y-x)=3t(3t+x)[/math] I have [math]x=\frac{9t^2-y^2}{3t+y}[/math] Is this the simplest form?

The idea of increase and decrease leads to numbers and counting. Numbers lead to the idea of combination, of function within measure. Functions lead to “functions within functions”, and there is a projection, in both directions. Number maps to function, function maps to function within function (combination, transitivity, commutation), and on up the chain. Math is like a big chain. Where do numbers come from? We all understand “less”, “more”, and “same”, in terms of measurement. At first, human measurement of the environment was probably largely restricted to these ideas of (available) information. Gradually, a need would have developed to record information in ways …