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Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)

 
reversefiction
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User ID: 25019064
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04/06/2013 09:27 PM

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Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)
All right, so I'm working through my calculus homework, and I encounter a problem such as lim n -> infinity of ln 1/n... The limit is 0. So, we get ln 0. Which is undefined. However my book tells me that the limit is negative infinity. How is that possible? Because if we convert the ln 0 back into an exponent we get. e^x = 0. And we all know that there is no solution for this problem. I'm curious how this works.
// My definition of insanity.

bool try() { return false; }

void insanity() {

bool success = false;
while(!success) {
if(try()) {
break;
}
}
}
Anonymous Coward
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04/06/2013 09:32 PM
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Re: Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)
wut? can you just straight out ask what the question is
Anonymous Coward
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04/06/2013 09:32 PM
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Re: Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)
Suppose you try calculating a few logs and see what happens:

(here l is the natural log function)

l(1/1)
0
l(1/10)
-2.30258509299404568401
l(1/100)
-4.60517018598809136803
l(1/1000)
-6.90775527898213705205
l(1/10000)
-9.21034037197618273607
l(1/1000000)
-13.81551055796427410410
l(1/1000000000)
-20.72326583694641115616
l(1/1000000000000)
-27.63102111592854820821

you can see that the result of the natural log function gets smaller as n gets bigger. It sure looks like it might be approaching negative infinity, doesn't it?
Anonymous Coward
User ID: 37530446
Australia
04/06/2013 09:33 PM
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Re: Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)
When the hell are you EVER going to need to use these math calculations later on?
Chuck

User ID: 37522283
United States
04/06/2013 09:34 PM
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Re: Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)
Because ln n is basically equivalent to e^x=n. So, if n is approaching 0, x is approaching neg. infinity (damn ascii). Any more questions?

Last Edited by Chuck on 04/06/2013 09:37 PM
reversefiction (OP)

User ID: 25019064
United States
04/06/2013 09:35 PM

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Re: Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)
Suppose you try calculating a few logs and see what happens:

(here l is the natural log function)

l(1/1)
0
l(1/10)
-2.30258509299404568401
l(1/100)
-4.60517018598809136803
l(1/1000)
-6.90775527898213705205
l(1/10000)
-9.21034037197618273607
l(1/1000000)
-13.81551055796427410410
l(1/1000000000)
-20.72326583694641115616
l(1/1000000000000)
-27.63102111592854820821

you can see that the result of the natural log function gets smaller as n gets bigger. It sure looks like it might be approaching negative infinity, doesn't it?
 Quoting: Anonymous Coward 37573475


Ahh, Thank you! My calculus teacher doesn't let us use a calculator on anything. So, I'm so used to going without. I think I've been doing homework for too long today. It might be beer thirty. :)
// My definition of insanity.

bool try() { return false; }

void insanity() {

bool success = false;
while(!success) {
if(try()) {
break;
}
}
}
Astral Goat
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User ID: 33435073
United States
04/06/2013 09:35 PM

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Re: Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)
Suppose you try calculating a few logs and see what happens:

(here l is the natural log function)

l(1/1)
0
l(1/10)
-2.30258509299404568401
l(1/100)
-4.60517018598809136803
l(1/1000)
-6.90775527898213705205
l(1/10000)
-9.21034037197618273607
l(1/1000000)
-13.81551055796427410410
l(1/1000000000)
-20.72326583694641115616
l(1/1000000000000)
-27.63102111592854820821

you can see that the result of the natural log function gets smaller as n gets bigger. It sure looks like it might be approaching negative infinity, doesn't it?
 Quoting: Anonymous Coward 37573475


good work
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Anonymous Coward
User ID: 17952489
United States
04/06/2013 09:37 PM
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Re: Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)
Suppose you try calculating a few logs and see what happens:

(here l is the natural log function)

l(1/1)
0
l(1/10)
-2.30258509299404568401
l(1/100)
-4.60517018598809136803
l(1/1000)
-6.90775527898213705205
l(1/10000)
-9.21034037197618273607
l(1/1000000)
-13.81551055796427410410
l(1/1000000000)
-20.72326583694641115616
l(1/1000000000000)
-27.63102111592854820821

you can see that the result of the natural log function gets smaller as n gets bigger. It sure looks like it might be approaching negative infinity, doesn't it?
 Quoting: Anonymous Coward 37573475


Ahh, Thank you! My calculus teacher doesn't let us use a calculator on anything. So, I'm so used to going without. I think I've been doing homework for too long today. It might be beer thirty. :)
 Quoting: reversefiction


Shitty. I wouldn't have made it through engineering school without my ti-89. Don't ask me to do long division though...
Anonymous Coward
User ID: 37573475
Australia
04/06/2013 09:40 PM
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Re: Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)
Suppose you try calculating a few logs and see what happens:

(here l is the natural log function)

l(1/1)
0
l(1/10)
-2.30258509299404568401
l(1/100)
-4.60517018598809136803
l(1/1000)
-6.90775527898213705205
l(1/10000)
-9.21034037197618273607
l(1/1000000)
-13.81551055796427410410
l(1/1000000000)
-20.72326583694641115616
l(1/1000000000000)
-27.63102111592854820821

you can see that the result of the natural log function gets smaller as n gets bigger. It sure looks like it might be approaching negative infinity, doesn't it?
 Quoting: Anonymous Coward 37573475


Ahh, Thank you! My calculus teacher doesn't let us use a calculator on anything. So, I'm so used to going without. I think I've been doing homework for too long today. It might be beer thirty. :)
 Quoting: reversefiction

hey i didn't use a calculator! i used a computer and ran the gnu "bc" program:

[link to www.gnu.org]

if you think about what logarithms and exponents mean, i think you will figure out that the log of a number between zero and one has to get smaller as the number approaches zero.

think about the meaning of the number 10^-2 in terms of logarithms. then think about 10^-3, 10^-4, and so on. then relate that to 1/100, 1/1000, 1/10000, and so on.

then relate the fractions 1/100 and so on to the original calculus question, and it will hopefully be pretty obvious what the correct answer is.
Anonymous Coward
User ID: 29941383
United States
04/06/2013 09:42 PM
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Re: Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)
OP, here is what you need:

The natural log of a fraction is this:

ln(a/b) = ln(a) - ln(b)

ln(1/n) = ln(1) - ln(n)

ln(1) = 0

ln(1/n) = -ln(n)

lim(n->infinity) ln(1/n) = -ln(n) = -infinity
reversefiction (OP)

User ID: 25019064
United States
04/06/2013 09:50 PM

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Re: Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)
Suppose you try calculating a few logs and see what happens:

(here l is the natural log function)

l(1/1)
0
l(1/10)
-2.30258509299404568401
l(1/100)
-4.60517018598809136803
l(1/1000)
-6.90775527898213705205
l(1/10000)
-9.21034037197618273607
l(1/1000000)
-13.81551055796427410410
l(1/1000000000)
-20.72326583694641115616
l(1/1000000000000)
-27.63102111592854820821

you can see that the result of the natural log function gets smaller as n gets bigger. It sure looks like it might be approaching negative infinity, doesn't it?
 Quoting: Anonymous Coward 37573475


Ahh, Thank you! My calculus teacher doesn't let us use a calculator on anything. So, I'm so used to going without. I think I've been doing homework for too long today. It might be beer thirty. :)
 Quoting: reversefiction

hey i didn't use a calculator! i used a computer and ran the gnu "bc" program:

[link to www.gnu.org]

if you think about what logarithms and exponents mean, i think you will figure out that the log of a number between zero and one has to get smaller as the number approaches zero.

think about the meaning of the number 10^-2 in terms of logarithms. then think about 10^-3, 10^-4, and so on. then relate that to 1/100, 1/1000, 1/10000, and so on.

then relate the fractions 1/100 and so on to the original calculus question, and it will hopefully be pretty obvious what the correct answer is.
 Quoting: Anonymous Coward 37573475


OP, here is what you need:

The natural log of a fraction is this:

ln(a/b) = ln(a) - ln(b)

ln(1/n) = ln(1) - ln(n)

ln(1) = 0

ln(1/n) = -ln(n)

lim(n->infinity) ln(1/n) = -ln(n) = -infinity
 Quoting: Anonymous Coward 29941383


USA.. Thanks man just like what you learn in algebra :) And it makes a lot of sense.

Australia... Yeah, I guess after you answered it I blushed a little bit, because I realized it was a pretty elementary question. It's just the last 9 weeks have been all integrals, and now finally were getting back into doing series and sequences. More "real" math, instead of trying to find the anti-derivative.
// My definition of insanity.

bool try() { return false; }

void insanity() {

bool success = false;
while(!success) {
if(try()) {
break;
}
}
}
Chuck

User ID: 37522283
United States
04/06/2013 09:56 PM
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Re: Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)
Wait til Calc 3 and Green's Theorem and all of this will seem elementary.
reversefiction (OP)

User ID: 25019064
United States
04/06/2013 10:00 PM

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Re: Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)
Wait til Calc 3 and Green's Theorem and all of this will seem elementary.
 Quoting: Chuck


I just looked that up. Is the integral of an integral like finding y'' just in reverse?
// My definition of insanity.

bool try() { return false; }

void insanity() {

bool success = false;
while(!success) {
if(try()) {
break;
}
}
}
Anonymous Coward
User ID: 33560264
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04/06/2013 10:00 PM
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Re: Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)
When the hell are you EVER going to need to use these math calculations later on?
 Quoting: Anonymous Coward 37530446


Several area, it also helps the mind solve issues quicker. Critical thinking...
reversefiction (OP)

User ID: 25019064
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04/06/2013 10:17 PM

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Re: Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)
When the hell are you EVER going to need to use these math calculations later on?
 Quoting: Anonymous Coward 37530446


Several area, it also helps the mind solve issues quicker. Critical thinking...
 Quoting: Anonymous Coward 33560264


An understanding of math brings something that is so rare in our society today. Discipline of the mind. Maybe you can find that in transcendental meditation, or some sort of yoga. But for western thinkers mathematics has been the means in which our minds have grown and excelled. When you take a math class, your seeing literally the best of what human kind has accomplished. Because, without mathematics. Many of the pleasures that you enjoy today from technology would have never been created otherwise. The thing about math is, math is a universal language. Anyone who has studied mathematics could read my math notes and understand what they mean. That's not the same for the notes I've taken in other classes. Because, those are limited to English.
// My definition of insanity.

bool try() { return false; }

void insanity() {

bool success = false;
while(!success) {
if(try()) {
break;
}
}
}
Anonymous astrophysicst
User ID: 1550396
United States
06/23/2013 02:11 AM
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Re: Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)
When the hell are you EVER going to need to use these math calculations later on?
 Quoting: Anonymous Coward 37530446


Several area, it also helps the mind solve issues quicker. Critical thinking...
 Quoting: Anonymous Coward 33560264


An understanding of math brings something that is so rare in our society today. Discipline of the mind. Maybe you can find that in transcendental meditation, or some sort of yoga. But for western thinkers mathematics has been the means in which our minds have grown and excelled. When you take a math class, your seeing literally the best of what human kind has accomplished. Because, without mathematics. Many of the pleasures that you enjoy today from technology would have never been created otherwise. The thing about math is, math is a universal language. Anyone who has studied mathematics could read my math notes and understand what they mean. That's not the same for the notes I've taken in other classes. Because, those are limited to English.
 Quoting: reversefiction


I don't totally disagree, because complex math trains te brain to solve complex problems. however, one must keep in mind tat like a computer the human brain does not have an infinite ability to store and process information.

For this reason if a person absorbs to much worthless information that will never apply to any real life situation like we see with the more advanced calculus exercises, eventually there is going to be less 'room' for other information. This is why individuals on the PD level always specialize in an extremely narrow field of study. The problem with this is, they become blinded to the interactions between the various intellectual disciplines and therefore very limited in their ability to perform truly useful tasks, since they do not and cannot see "the whole picture". Personally, I do not think that any REAL problem can be solved with calculus and that those who think they have always must concede their conclusions are theoretical and not carved in stone fact.

The purpose of mathematics in any intellectual exercise should be to quantify, measure and confirm real life observations and to calculate unknowns based on established and faultless patterns., not make definitive conclusions directly from mathematics alone. When you get into negative infinities and equations with 0 involved, you are engaging in a totally useless intellectual exercise that as op pointed out , make no sense and have no bearing on any reality..

Everyone who has attempted to has failed.
cisdac

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06/23/2013 02:34 AM
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Re: Serious Math Question. Need a serious math nerd to help explain this to me. (Involves Calc)
These aren't the droids you're looking for.

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