Search found 238 matches

by Mike_Bson
Thu Mar 31, 2011 10:14 am UTC
Forum: Mathematics
Topic: What is your favorite proof?
Replies: 41
Views: 4867

Re: What is y'all's favorite proof?

My favorite is definitely using differential equation to prove Euler's Formula. If f(x) = e^(ix), then f'(x) = i*e^(ix) = i*f(x). If f(x) = cos(x) + isin(x), then f'(x) = -sin(x) + icos(x) = i*f(x). So these both are solutions to the differential equation y' - iy = 0, and they both satisfy f(0) = 1....
by Mike_Bson
Thu Feb 03, 2011 7:03 pm UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 468323

Re: Favorite math jokes

i is being such a hypocrite, considering it is not a rational number.
by Mike_Bson
Sat Jan 29, 2011 6:49 am UTC
Forum: Mathematics
Topic: Integral of 1/x
Replies: 10
Views: 3343

Re: Integral of 1/x

antonfire wrote:An even more minor point: there are antiderivatives of 1/x on R\{0} which are not of the form ln(x) + C.

Such as?
by Mike_Bson
Wed Jan 19, 2011 8:00 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0849: "Complex Conjugate"
Replies: 96
Views: 22663

Re: 0849: "Complex Conjugate"

I hate complex numbers. I mean, calculus was hard enough to begin with, why the hell did they have to go and invent imaginary numbers? Were they deprived of imaginary friends as children and now want to get back at the rest of the world? Moments like this make me feel like the only person in the wo...
by Mike_Bson
Wed Jan 19, 2011 5:34 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0849: "Complex Conjugate"
Replies: 96
Views: 22663

Re: 0849: "Complex Conjugate"

Since I love complex analysis, this is my new favorite comic.
by Mike_Bson
Tue Jan 18, 2011 9:06 pm UTC
Forum: Mathematics
Topic: Math Books
Replies: 378
Views: 253073

Re: Math Books

Is Elementary Linear Algebra by Howard Anton a good book for beginning Linear Algebra?
by Mike_Bson
Mon Jan 17, 2011 4:53 am UTC
Forum: Mathematics
Topic: Nerd alert (messing around with the quadratic formula)
Replies: 25
Views: 2789

Re: Nerd alert (messing around with the quadratic formula)

Nitrodon wrote:
Mike_Bson wrote:Also, if a Fibonacci prime is the nth Fibonacci number, n is prime. For example, 89 is prime, and the 11th Fibonacci number.

There is exactly one number for which this statement does not hold.

Ah yes, F(4) = 3.
by Mike_Bson
Sun Jan 16, 2011 9:18 pm UTC
Forum: Mathematics
Topic: Negative numbers to non-integer powers
Replies: 5
Views: 2962

Re: Negative numbers to non-integer powers

Qaanol wrote:The one on the left is the twentieth root of 4, of which there, you know, 20 of them. The one on the right in the tenth root of -2, of which there are 10 of them.

Okay, I did not remember that. Thank you!
by Mike_Bson
Sun Jan 16, 2011 8:32 pm UTC
Forum: Mathematics
Topic: Negative numbers to non-integer powers
Replies: 5
Views: 2962

Re: Negative numbers to non-integer powers

Alright, I found an example where the property does not work:

[imath]((-2)^{2})^{0.05} \neq (-2)^{0.1}[/imath]
by Mike_Bson
Sun Jan 16, 2011 8:07 pm UTC
Forum: Mathematics
Topic: Nerd alert (messing around with the quadratic formula)
Replies: 25
Views: 2789

Re: Nerd alert (messing around with the quadratic formula)

The Fibonacci Sequence has an even number every third term? Sonofa... Also, if a Fibonacci number is the nth number, n is prime. For example, 89 is prime, and the 11th Fibonacci number. I don't quite get this one. The nth number of what sequence? Sorry, I meant to say: Also, if a Fibonacci prime is...
by Mike_Bson
Sun Jan 16, 2011 7:38 pm UTC
Forum: Mathematics
Topic: Nerd alert (messing around with the quadratic formula)
Replies: 25
Views: 2789

Re: Nerd alert (messing around with the quadratic formula)

thicknavyrain wrote:
mdyrud wrote:The Fibonacci Sequence has an even number every third term?


Sonofa...

Also, if a Fibonacci number is the nth number, n is prime. For example, 89 is prime, and the 11th Fibonacci number.
by Mike_Bson
Sun Jan 16, 2011 7:19 pm UTC
Forum: Mathematics
Topic: Nerd alert (messing around with the quadratic formula)
Replies: 25
Views: 2789

Re: Nerd alert (messing around with the quadratic formula)

Even though the result is a unwieldy and probably not terribly useful, good job. One of the best ways to get better at math is exposing yourself to it, and it sounds like this is a really good way to give some great practice with rearranging equations. So don't worry about justifying yourself. Embr...
by Mike_Bson
Sun Jan 16, 2011 5:57 pm UTC
Forum: Mathematics
Topic: Negative numbers to non-integer powers
Replies: 5
Views: 2962

Re: Negative numbers to non-integer powers

((-0.5)^2)^{3.2} = (-0.5)^{6.4} = (-0.5^6) * (-0.5^{0.2}) * (-0.5^{0.2}) \approx -0.015625 * -0.8705506 * -0.8705506 = -0.0118415 That's why you got a real number for that one. You can take the 5th root of a negative, but taking the square root will g...
by Mike_Bson
Sat Jan 01, 2011 11:23 am UTC
Forum: Mathematics
Topic: Questions about sets
Replies: 18
Views: 2867

Re: Questions about sets

Alright, I finally completely understand it. Thank you guys so much for your help!
by Mike_Bson
Fri Dec 31, 2010 10:25 pm UTC
Forum: Mathematics
Topic: Questions about sets
Replies: 18
Views: 2867

Re: Questions about sets

Okay, that makes more sense to me. What is an example of a set with the cardinality \aleph_1 , then? And what about \aleph_2 ? EDIT- Wait, \aleph_1 would be the set of all ordinal numbers I listed, i.e. the countable ones, right? Alright, now I just want an example of \aleph_2 . Also, I assume \epsi...
by Mike_Bson
Fri Dec 31, 2010 9:27 pm UTC
Forum: Mathematics
Topic: Questions about sets
Replies: 18
Views: 2867

Re: Questions about sets

So, let me get this straight: [imath]\aleph_0[/imath] the cardinality of the set of all of the ordinals up to [imath]\omega \times 2[/imath], [imath]\aleph_1[/imath] is the cardinality of the set of all ordinals up to [imath]\omega^2[/imath], [imath]\aleph_2[/imath] is the cardinality of all ordinals up to [imath]\omega^\omega[/imath], etc.? Do I have this right?
by Mike_Bson
Fri Dec 31, 2010 1:34 am UTC
Forum: Mathematics
Topic: Questions about sets
Replies: 18
Views: 2867

Re: Questions about sets

1. I know \aleph_1 is defined as the cardinality of the set of ordinal numbers. Interestingly, there is no set of ordinal numbers. This is called the Burali-Forti paradox on wikipedia. If there were a set of all ordinal numbers, the union of this set would be an ordinal. In ZFC, a set is not allowe...
by Mike_Bson
Thu Dec 30, 2010 11:05 am UTC
Forum: Mathematics
Topic: Questions about sets
Replies: 18
Views: 2867

Re: Questions about sets

Could you give me an example of a set with a cardinality of [imath]\aleph_1[/imath] and one with [imath]\aleph_2[/imath]?

EDIT- And what cardinality is the set of reals?
by Mike_Bson
Thu Dec 30, 2010 6:54 am UTC
Forum: Mathematics
Topic: Questions about sets
Replies: 18
Views: 2867

Re: Questions about sets

Would you kindly tell me what the difference between the set of ordinals and the set of countable ordinals is? Thanks for your help.
by Mike_Bson
Thu Dec 30, 2010 5:30 am UTC
Forum: Mathematics
Topic: Questions about sets
Replies: 18
Views: 2867

Questions about sets

1. I know \aleph_1 is defined as the cardinality of the set of ordinal numbers. What I ask is, consider this set: a countable set, whose members are countable sets. An example of this would be this set: {{1}, {2}, {3}, {4}, . . .}, where {1} is the set of all of the multiples of 1, {2} is the set of...
by Mike_Bson
Mon Dec 20, 2010 11:34 pm UTC
Forum: Mathematics
Topic: ln(x) or log(x)?
Replies: 63
Views: 8587

Re: ln(x) or log(x)?

I think it's similar to degrees/radians... when first teaching trig, everything's done in degrees, because that's what the students would be familiar with. Trying to introduce radians at this point would just result in a lot of "but... why?". But then when you get to calculus, or complex ...
by Mike_Bson
Sun Dec 19, 2010 1:12 am UTC
Forum: Mathematics
Topic: Crazy numbers
Replies: 17
Views: 3495

Re: Crazy numbers

Diadem wrote:This does mean that |1 + c| = 0. That's rather strange :)

That is what I was conjecturing. Thanks for the proof, though, I like your definition of these.
by Mike_Bson
Sun Dec 19, 2010 12:49 am UTC
Forum: Mathematics
Topic: ln(x) or log(x)?
Replies: 63
Views: 8587

Re: ln(x) or log(x)?

Diadem wrote:I actually consciously made that choice as a way of saying "I may be a physicist, but I do enjoy mathematics a lot".

I said something like, ''I don't give a damn about base 10, so I won't dignify it by saying ln.''
by Mike_Bson
Sun Dec 19, 2010 12:42 am UTC
Forum: Mathematics
Topic: Crazy numbers
Replies: 17
Views: 3495

Re: Crazy numbers

What is |1 + c|?
by Mike_Bson
Sat Dec 18, 2010 10:58 pm UTC
Forum: Mathematics
Topic: inflection points of x^(1/x)
Replies: 13
Views: 2338

Re: inflection points of x^(1/x)

But really, e=\sqrt[i\pi]{-1} . Which is begging the question: what IS the i*pi th root of something? How do you define that without resorting to using e or some other definition that depends on it? x^(1/(pi*i))? Yeah, but what the hell does that even MEAN? This is the problem, how can you define w...
by Mike_Bson
Sat Dec 18, 2010 10:57 pm UTC
Forum: Mathematics
Topic: Why octal is better than decimal
Replies: 64
Views: 9815

Re: Why octal is better than decimal

I'd rather have base 16.
by Mike_Bson
Sat Dec 18, 2010 6:54 pm UTC
Forum: Mathematics
Topic: inflection points of x^(1/x)
Replies: 13
Views: 2338

Re: inflection points of x^(1/x)

LLCoolDave wrote:
Mindworm wrote:
But really, [imath]e=\sqrt[i\pi]{-1}[/imath].


Which is begging the question: what IS the i*pi th root of something? How do you define that without resorting to using e or some other definition that depends on it?

x^(1/(pi*i))?
by Mike_Bson
Sat Dec 18, 2010 2:04 am UTC
Forum: Mathematics
Topic: ln(x) or log(x)?
Replies: 63
Views: 8587

Re: ln(x) or log(x)?

In complex analysis, the complex logarithm is defined using the real logarithm, i.e. Log z := ln r + iθ = ln | z | + iArg z I am a noob to complex analysis. Would you kindly inform me the difference of saying Log(z) and ln(r)? Like, I know the former is the log of a complex number, and the latter r...
by Mike_Bson
Sat Dec 18, 2010 1:45 am UTC
Forum: Mathematics
Topic: ln(x) or log(x)?
Replies: 63
Views: 8587

Re: ln(x) or log(x)?

If you work with log base e, you don't have all these nice properties, and the intuition is less clear when learning it for the first time. Or just write log 10 (x) when teaching kids about logarithms to build this intuition. In fact, that seems like such a trivial matter, it shouldn't have anythin...
by Mike_Bson
Sat Dec 18, 2010 1:21 am UTC
Forum: Mathematics
Topic: ln(x) or log(x)?
Replies: 63
Views: 8587

ln(x) or log(x)?

Note- This seems like the thing that there would probably be another older thread on, but my searching results turned out to be inconclusive. If this is a repeat post, I apologize. After getting in a multitude of debacles on this, I have decided to seek our the XKCD fora for their views. So, I ask y...
by Mike_Bson
Thu Dec 16, 2010 2:53 am UTC
Forum: Mathematics
Topic: Anyone know/have a proof for this?
Replies: 4
Views: 882

Re: Anyone know/have a proof for this?

This fact can be derived from the Laurent series for \zeta(s) about 1. This series is {1 \over s-1} + \gamma + \gamma_1(s-1) + \gamma_2(s-1)^2 + \cdots, where \gamma_1, \gamma_2, \dots are various real constants. Observe that if you plug in 1 + ix , all the terms are pure im...
by Mike_Bson
Thu Dec 16, 2010 1:52 am UTC
Forum: Mathematics
Topic: Anyone know/have a proof for this?
Replies: 4
Views: 882

Anyone know/have a proof for this?

I was messing around, when I found a little fact on WolframAlpha which I find extremely interesting:

Here

So, does anyone know/have the proof for this? I have searched high and low for it.
by Mike_Bson
Sat Nov 27, 2010 6:54 am UTC
Forum: Mathematics
Topic: To what does this series evaluate?
Replies: 12
Views: 2174

Re: To what does this series evaluate?

Unfortunately, "most" sums don't have closed form expressions. It's likely (though probably hasn't been shown) that this one doesn't. Chances are, the best you can do is relate it to other esoteric expressions . Hm, the relationship with that definite integral is indeed interesting. Could...
by Mike_Bson
Fri Nov 26, 2010 4:53 am UTC
Forum: Mathematics
Topic: To what does this series evaluate?
Replies: 12
Views: 2174

To what does this series evaluate?

This is just a problem I have been curious about: \sum_{k=1}^{\infty} k^{-k} I've been trying to evaluate this for the exact value for a few hours. I know this converges to about 1.291285997, but I'm trying to find the exact value; does anyone know the answer, or a way to find the answer? I've tried...
by Mike_Bson
Wed Nov 24, 2010 9:20 pm UTC
Forum: Mathematics
Topic: Disguised forms of 2
Replies: 114
Views: 12123

Re: Disguised forms of 2

@Ebester Quartic formula much? Glad it only exists when the degree is less than or equal to four, any higher and you'd just be unleashing hell on us. . . There is a formula that can solve any solvable quintic and was apparently printed in one book in 2004 on three whole pages. I can't get my hands ...
by Mike_Bson
Tue Nov 23, 2010 4:17 am UTC
Forum: Mathematics
Topic: Have You Been Taught Things Which Aren't True?
Replies: 97
Views: 15638

Re: Have You Been Taught Things Which Aren't True?

I learned about nullity in 3rd grade.
by Mike_Bson
Mon Nov 22, 2010 7:21 pm UTC
Forum: Mathematics
Topic: L'Hospital's Rule, or l'Hopital's rule?
Replies: 10
Views: 5362

Re: L'Hospital's Rule, or l'Hopital's rule?

Velifer wrote:It's spelled like this:
Bernoulli's Rule.

My amateur mathematician brain does not get it. Explain?

Edit- Never mind, looked it up. I think I'd rather call it that anyway.
by Mike_Bson
Mon Nov 22, 2010 1:53 am UTC
Forum: Mathematics
Topic: Disguised forms of 2
Replies: 114
Views: 12123

Re: Disguised forms of 2

@Ebester

Quartic formula much? Glad it only exists when the degree is less than or equal to four, any higher and you'd just be unleashing hell on us. . .
by Mike_Bson
Sun Nov 21, 2010 12:46 am UTC
Forum: Mathematics
Topic: L'Hospital's Rule, or l'Hopital's rule?
Replies: 10
Views: 5362

Re: L'Hospital's Rule, or l'Hopital's rule?

From the wiki page on the Marquis de l'Hôpital (after which the rule was named): In the 17th and 18th centuries, the name was commonly spelled "l'Hospital", however, French spellings have evolved: the silent 's' has been dropped and replaced with the circumflex over the preceding vowel. A...

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