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#76 Re: Dark Discussions at Cafe Infinity » 2015 UK General Election » 2019-04-30 09:09:12
The spam links in Mathegocart’s quote should be removed as well.
#77 Re: Dark Discussions at Cafe Infinity » The Yume thread » 2019-04-30 08:42:06
Last night I dreamed that my house was suddenly invaded by cats – which all came in through a gap in the wall of the bathroom.
#78 Re: Euler Avenue » More real numbers that natural numbers? » 2019-04-30 08:31:08
I think Cantor made a real mess of this field. In mapping the counting numbers (proportional to some finite limit N) to the rational numbers (proportional to the finite limite N²) he made infinity impossible to understand in logical terms. Because it is infinity, that doesn't make everything magically correct. You should be able to think of infinity as some value N which is CONSISTENTLY increased without restriction. He insisted on increasing N inconsistently and therefore came up with some rather foolish results.
Here is how I do it:
http://lesliegreen.byethost3.com/articles/new_maths.pdf
I sympathize with you; I myself have reservations about Cantor’s diagonal proof of the uncountability of the real numbers. For example, he seemed to assume that there was a bijection between each real number as its infinite decimal representation – this is not quite true, as seen by the fact that
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Here is how Jade Tan-Holmes does it on her YouTube channel Up and Atom: An Alternative Proof That The Real Numbers Are Uncountable.
#79 Re: Euler Avenue » What had you learned today that you found interesting? » 2019-04-29 19:26:51
I recently started learning about partial differential equations. The video gives the heat equation as an example of a PDE – and includes a fascinatingly watchable derivation of the equation discovered by Joseph Fourier.
Another example of a PDE is the wave equation:
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where ψ(x,t) is the function of a one-dimensional wave with position x at time t and c is the speed of propagation of the wave. If the wave has amplitude A, frequency f and wavelength λ, then c = fλ and the wave function has a complex solution given by
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where ω = 2πf is the angular frequency and k = 2π/λ is the wavenumber. Note that:
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– that is to say, the motion of each point of the wave is simple harmonic.
#80 Re: Help Me ! » Co-prime numbers » 2019-04-29 18:30:47
hi;
If there is an equation satisying the relation:
and
How to prove that
is composite?
That is not true. Take, for example, n = 3, x = 5, m = 5, c = 3. Here, nx = mc and gcd(m,n) = 1 but c=3 is prime.
#81 Re: Help Me ! » [ASK] Proof of Some Quadratic Functions » 2019-04-08 07:40:55
6. The quadratic equation whose roots are squares of the roots of is x.
#82 Re: Help Me ! » Please help me with a proof » 2019-03-16 00:43:42
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#83 Puzzles and Games » Unsolvable Master Detective game » 2019-03-15 23:58:39
- Alg Num Theory
- Replies: 1
This game: https://www.mathsisfun.com/games/master-detective.html.
Is there a glitch in the software?
If there is a glitch, please fix it. I’ve just wasted four hours of my morning trying to solve an unsolvable game.
Thanks.
#84 Re: Dark Discussions at Cafe Infinity » Words that contain AEIOU, in any order, each vowel exactly once » 2019-02-25 09:52:36
JaneFairfax wrote:UOIAE
fluoridate
fluorinate
subordinate
uncomplicated
unprofitable
unsociableunmotivated
glucosidase
#85 Re: Dark Discussions at Cafe Infinity » Why is there something instead of nothing? » 2018-10-23 06:19:19
Q: What do you take when you have a headache?
A: Take nothing – because nothing acts faster than Anadin!
Similarly, if you want to be perfect, be nobody – because nobody is perfect!
#86 Re: Euler Avenue » A proof of the Riemann hypothesis » 2018-09-24 08:33:09
Sir Michael Francis Atiyah … is a British-Lebanese mathematician specialising in geometry.
At a hotly-anticipated talk at the Heidelberg Laureate Forum today [Monday 24 September 2018], retired mathematician Michael Atiyah delivered what he claimed was a proof of the Riemann hypothesis, a challenge that has eluded his peers for nearly 160 years.
#87 Re: This is Cool » Interesting facts » 2018-08-26 23:20:39
#89 Re: This is Cool » Interesting facts » 2018-08-11 05:22:05
#90 Re: Puzzles and Games » Playing with natural numbers and SQRT » 2018-08-10 05:18:54
If a = 2, b = 1, c = 4, then A = √(2+1·√ 4) = 2, B = √(2−1·√ 4) = 0, S = A + B = 2 ≠ b.
#91 Re: Help Me ! » Inductive and Deductive Reasoning » 2018-07-31 00:25:10
Draw three distinct, parallel lines and another line (a transversal) to cross them all.
But those three lines may not be in one and the same plane.
#92 Re: Help Me ! » Conditional Statements and Venn Diagrams » 2018-07-28 16:11:31
Let x be the number of people enrolled in all three classes. Then:
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Now that you have split the numbers into non-overlapping groups, you can add them up:
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#93 Re: Help Me ! » Find all real solutions: Proof help » 2018-07-28 02:29:13
Let us apply zetafunc’s method in another way. Dividing by 2 and rearranging gives
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Now consider the following table:
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Thus we see that outside of {0,±1} the equation has no solution as the LHS and RHS have opposite signs. This proves that there are no solutions other than x = 0, ±1.
#94 Re: Help Me ! » Find all real solutions: Proof help » 2018-07-26 23:44:22
There are precisely three solutions:
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Unfortunately I do not know how to prove it rigorously. Maybe Bob Bundy can come up with more helpful information.
#95 Re: Formulas » Tests For Divisibility » 2018-07-24 10:21:40
Here’s a YouTube video on tests of divisibility and how to apply them to some math problems.
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I found the solution to finding all palindromic four-digit powers particularly interesting.
#96 Re: Help Me ! » A cubic eq. » 2018-07-24 06:09:34
Can you help me solve this equation?
#97 Re: Exercises » Mathematical Induction » 2018-07-15 20:35:17
What do you mean by why is n term not 2n−1?
Since the thread title is mathematical induction, I take it you want to prove the formula for the sum of the first n odd positive integers. To do this, you need to know what the formula is in the first place. If you’re not given the formula, you can make a guess and then proceed to prove it. So, trying the first few sums …
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I think you can make a guess as to what the formula is going to be.
#98 Re: Exercises » Quadratic » 2018-07-15 00:12:13
I presume ɑ and β are the roots, which are complex. Since we are going to deal with their powers, best to convert them to cos–sin form:
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So the roots are
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one of them is ɑ, the other is β. Since the question doesn’t say which is which, you may as well take your pick. Now use De Moivre’s theorem.
#99 Re: This is Cool » A difficult problem from 1957 » 2018-07-14 22:41:52
Why can’t they use metric?
#100 Re: Help Me ! » Division » 2018-07-04 21:59:22
Do the long division yourself!