It’s a bit disappointing that people think linking to wikipedia is preferrable to some kind of discussion, or that it’s a reliable enough source to settle an argument. Although with mathematics most articles are on topics obscure enough not to warrant vandalism, and are usually written by experts.
Tell me exactly why the same explanation (hypothetically) typed out here would be valid, but if it’s typed out on Wikipedia it cannot be or likely is not a good answer and should be ignored or given less credit than if typed out here.
As to your reliance on authority rather than the argument itself when it comes to mathematics, I can’t help you there. Myself, I don’t care if it’s a baboon that presents a sound argument. It’s the argument that matters, not the source. To me that is, but from your post it would seem not to you, which of course is your right.
Well, that’s a bit of a straw man argument isn’t it? What I’m saying is that wikipedia is often reliable for niche topics, that only people with considerable interest and knowledge would write or edit, but it can often be very unreliable. For example, sometimes users decide that they really know best about an article, and will revert any edits they don’t like, however valid they are.
I’m just questioning why people think posting a link to an online encyclopedia is sufficient to answer any question. I’m not saying in this case it isn’t right, but at least people were talking about their ideas. And I’d rather have people thinking about mathematics than just taking somebody’s word for it.
[quote]Rational Gaze wrote:
Well, that’s a bit of a straw man argument isn’t it? What I’m saying is that wikipedia is often reliable for niche topics, that only people with considerable interest and knowledge would write or edit, but it can often be very unreliable. For example, sometimes users decide that they really know best about an article, and will revert any edits they don’t like, however valid they are.
I’m just questioning why people think posting a link to an online encyclopedia is sufficient to answer any question. I’m not saying in this case it isn’t right, but at least people were talking about their ideas. And I’d rather have people thinking about mathematics than just taking somebody’s word for it.[/quote]
It offers some insight. Mathematics and physics abide by absolute laws and opinions cannot really be brought into a math argument. If it was politics or something abstract, where opinions on a subject can vary because it depends on the input of the individual or situation (can murder always be justified, is socialism better than democracy, etc ?), then i would understand your argument.
However, when it refers to mathematics, then i think wikipedia is fine.
edit: I’m not advocating laziness. If someone tries to understand something and cannot, then using exterior sources such as dr.math or wikipedia, then that is acceptable.
[quote]Rational Gaze wrote:
Well, that’s a bit of a straw man argument isn’t it? What I’m saying is that wikipedia is often reliable for niche topics, that only people with considerable interest and knowledge would write or edit, but it can often be very unreliable. For example, sometimes users decide that they really know best about an article, and will revert any edits they don’t like, however valid they are.
I’m just questioning why people think posting a link to an online encyclopedia is sufficient to answer any question. I’m not saying in this case it isn’t right, but at least people were talking about their ideas. And I’d rather have people thinking about mathematics than just taking somebody’s word for it.[/quote]
You’re missing the point entirely. The point was that whether or not a poster here on the board could have answered the question, a link was posted that answered the question more then adequately. At that point the posts that followed should have, if nothing else, been comments on the link, not incorrect conjectures from people who probably shouldn’t have commented in the first place. Maybe even a simpler or more concise answer from a poster would have been appropriate, since neither link really provided a concise answer.
Bill was frustrated because even though the link was posted, posts followed from people who hadn’t even looked at the link or followed the thread. Curiously enough, even after Bills post another response popped up from someone with an (incorrect) answer who evidently didn’t read the link or any of the other replies.
[quote]ukrainian wrote:
stokedporcupine8 wrote:
ukrainian wrote:
Liv92 wrote:
You guys are tools, just saying…
Hey, I do find math interesting. I don’t understand how this would make me a tool.
stokedporcupine8, thank you for the information.
I think he meant we’re tools for kissing Debra’s ass 
If not though, it’s his loss and your gain. There is a wonderful and rich conceptual world to mathematics. You only get the tiniest taste of it from highschool algebra and a normal calculus series.
I did just finish AP Calc BC, so I get to do Calc 3/Diff Eq now as a Junior. Luckily, I have always found solving math equations and just doing Calculus quite entertaining.[/quote]
That’s cool. I wish that I had already been at that point when I was a highschool junior. I didn’t even start calculus until I was in college. You will probably have to wait until you get to college, but at some point there will be some major conceptual shifts in your math classes. Your math classes will go from being centered around solving equations to proofs, you’ll deal more with set theory and overall will take a more structural approach to things.
Hopefully if you have good teachers they will prepare you for this sort of thing, and not just have taught you how to mindless crank out derivatives.
In any case, I’m not quite sure what you’ll actually be doing in your Calc 3/Diff Eq class, but I found multivariable and vector calculus much more fun then the single variable stuff they teach you in calc 1 and 2. As for diff Eq, I think it’s slow going and boring at first, but by they time you get to partials it’s more fun.
By the way, to the OP, that really was a very interesting question. I’m not talented in mathematics unfortunately, but interesting things such as this are appreciated. It wasn’t a question I’d ever considered and while when explained properly, it’s clear enough, I sure wouldn’t have thunk it up.
Regarding Wikipedia, I know it has its share of faults, but generally I’ve found the science and math entries to be some of the best on the web – especially when it comes to explaining things in a more layman-style. Most likely because those entries don’t attract the typical web vandal.
I’m not really going to add to the real argument, but get used to not having an analytical answer, the real world doesn’t.
In the real world there is no 2 + 2 = 4.
I give a vendor that does casting stacked dimensions that add up to 4 and then talk about surface finish, casting method, material specs, tolerance, inspection dimensions, heating characteristics, cooling methods, est, est, est.
In the history of the world there has never been an exact measure of any facet of material properties and scientifically never can be.
Scientific “laws” and analytical methods must always be taken with a grain of salt. All human achievements in the physical world have been accomplished entirely by estimation and use of the rule of thumb, not the rule of laws.
For instance, all current structure analysis is done by simplifying any complex structure into and estimation of thousands (or millions) of simple beams and then throwing enough computing power at it to numerically (approximately) solve the ridiculous numbers of simultaneous equations. Essentially all FEA done today is based the elementary (and impossible) situation of a simple beam, the analytical model is not fancy.
But once again there has never been a physical situation with an analytical solution.
If there is a rule of law of the physical world, we don’t know it yet.
I do admit there are some situation analytical calculus has some uses. Inside electronics. Programming, signal processing, systems controls. But then only because the environment of the computer is not subject to the physical world.
But I’m an engineer, I’m biased.
[quote]ukrainian wrote:
stokedporcupine8 wrote:
ukrainian wrote:
Liv92 wrote:
You guys are tools, just saying…
Hey, I do find math interesting. I don’t understand how this would make me a tool.
stokedporcupine8, thank you for the information.
I think he meant we’re tools for kissing Debra’s ass
If not though, it’s his loss and your gain. There is a wonderful and rich conceptual world to mathematics. You only get the tiniest taste of it from highschool algebra and a normal calculus series.
I did just finish AP Calc BC, so I get to do Calc 3/Diff Eq now as a Junior. Luckily, I have always found solving math equations and just doing Calculus quite entertaining.[/quote]
Does AP calc allow you to skip certain courses? Such as first/some second year courses? If so I would suggest you don’t, unless you KNOW you can do the first year material blindfolded. I have people in my class, some of which have done IB and some who’ve done AP and a good deal of them failed our first year calc midterm (our final is in a few weeks, we’ll see what happens then). Maybe AP calc aligns better with the American university courses so I don’t really know.
[quote]DoubleDuce wrote:
I’m not really going to add to the real argument, but get used to not having an analytical answer, the real world doesn’t.
In the real world there is no 2 + 2 = 4.
I give a vendor that does casting stacked dimensions that add up to 4 and then talk about surface finish, casting method, material specs, tolerance, inspection dimensions, heating characteristics, cooling methods, est, est, est.
In the history of the world there has never been an exact measure of any facet of material properties and scientifically never can be.
Scientific “laws” and analytical methods must always be taken with a grain of salt. All human achievements in the physical world have been accomplished entirely by estimation and use of the rule of thumb, not the rule of laws.
For instance, all current structure analysis is done by simplifying any complex structure into and estimation of thousands (or millions) of simple beams and then throwing enough computing power at it to numerically (approximately) solve the ridiculous numbers of simultaneous equations. Essentially all FEA done today is based the elementary (and impossible) situation of a simple beam, the analytical model is not fancy.
But once again there has never been a physical situation with an analytical solution.
If there is a rule of law of the physical world, we don’t know it yet.
I do admit there are some situation analytical calculus has some uses. Inside electronics. Programming, signal processing, systems controls. But then only because the environment of the computer is not subject to the physical world.
But I’m an engineer, I’m biased.
[/quote]
These are some good points, but I’d like some clarification on some of your comments.
“In the history of the world there has never been an exact measure of any facet of material properties and scientifically never can be.”
Can you elaborate on this? As far as I know, all physical measurements are simply based on a human defined standard, for instance 1 second is defined as x number of orbits of an electron about a Cesium atom or something to that extent, and saying something like “5 seconds” simply gives a relative measurement with respect to that definition. The same holds for length, mass etc, so if this is true, then we can in fact obtain “exact” measurements by our own definition (Atomic clocks come to mind).
“Scientific “laws” and analytical methods must always be taken with a grain of salt. All human achievements in the physical world have been accomplished entirely by estimation and use of the rule of thumb, not the rule of laws.”
Are you referring to the use of approximation? If so then this seems similar to the point above, the theoretical models of things are only used as a reference point to which you compare a physical measurement, similar to how we compare a measurement of time to the definition of a second, we can compare a set of data to a definition of a function (for instance growth patterns of bacteria that follow exponential trends may not be exactly “2^n” but may be within an acceptable margin of error if approximated to that function using methods such as polynomial interpolation).
“I do admit there are some situation analytical calculus has some uses. Inside electronics. Programming, signal processing, systems controls. But then only because the environment of the computer is not subject to the physical world.”
The example of electronics, which you yourself gave IS subject to the physical world, and follows well known theoretical laws quite closely, unless what I’ve been taught is all wrong. Granted, analytically calculating things to very precise values requires extremely lengthy error analysis, like you said we can use computers to assist in this respect.
[quote]DoubleDuce wrote:
I’m not really going to add to the real argument, but get used to not having an analytical answer, the real world doesn’t.
In the real world there is no 2 + 2 = 4.
I give a vendor that does casting stacked dimensions that add up to 4 and then talk about surface finish, casting method, material specs, tolerance, inspection dimensions, heating characteristics, cooling methods, est, est, est.
In the history of the world there has never been an exact measure of any facet of material properties and scientifically never can be.
Scientific “laws” and analytical methods must always be taken with a grain of salt. All human achievements in the physical world have been accomplished entirely by estimation and use of the rule of thumb, not the rule of laws.
For instance, all current structure analysis is done by simplifying any complex structure into and estimation of thousands (or millions) of simple beams and then throwing enough computing power at it to numerically (approximately) solve the ridiculous numbers of simultaneous equations. Essentially all FEA done today is based the elementary (and impossible) situation of a simple beam, the analytical model is not fancy.
But once again there has never been a physical situation with an analytical solution.
If there is a rule of law of the physical world, we don’t know it yet.
I do admit there are some situation analytical calculus has some uses. Inside electronics. Programming, signal processing, systems controls. But then only because the environment of the computer is not subject to the physical world.
But I’m an engineer, I’m biased.
[/quote]
(1) The original question does admit of an “analytical” solution, it’s just that there are deeper, more foundation issues regarding which definition of the exponential function. Once one clears us those issues and picks some appropriate definition, the question admits of a simple analytic answer.
(2) I don’t really agree with the rest about physical laws at all, but I really don’t want to get into it. (EDITED)
But, I was a physics and math guy, I’m biased.
[quote]JLu wrote:
DoubleDuce wrote:
I’m not really going to add to the real argument, but get used to not having an analytical answer, the real world doesn’t.
In the real world there is no 2 + 2 = 4.
I give a vendor that does casting stacked dimensions that add up to 4 and then talk about surface finish, casting method, material specs, tolerance, inspection dimensions, heating characteristics, cooling methods, est, est, est.
In the history of the world there has never been an exact measure of any facet of material properties and scientifically never can be.
Scientific “laws” and analytical methods must always be taken with a grain of salt. All human achievements in the physical world have been accomplished entirely by estimation and use of the rule of thumb, not the rule of laws.
For instance, all current structure analysis is done by simplifying any complex structure into and estimation of thousands (or millions) of simple beams and then throwing enough computing power at it to numerically (approximately) solve the ridiculous numbers of simultaneous equations. Essentially all FEA done today is based the elementary (and impossible) situation of a simple beam, the analytical model is not fancy.
But once again there has never been a physical situation with an analytical solution.
If there is a rule of law of the physical world, we don’t know it yet.
I do admit there are some situation analytical calculus has some uses. Inside electronics. Programming, signal processing, systems controls. But then only because the environment of the computer is not subject to the physical world.
But I’m an engineer, I’m biased.
These are some good points, but I’d like some clarification on some of your comments.
“In the history of the world there has never been an exact measure of any facet of material properties and scientifically never can be.”
Can you elaborate on this? As far as I know, all physical measurements are simply based on a human defined standard, for instance 1 second is defined as x number of orbits of an electron about a Cesium atom or something to that extent, and saying something like “5 seconds” simply gives a relative measurement with respect to that definition. The same holds for length, mass etc, so if this is true, then we can in fact obtain “exact” measurements by our own definition (Atomic clocks come to mind).
“Scientific “laws” and analytical methods must always be taken with a grain of salt. All human achievements in the physical world have been accomplished entirely by estimation and use of the rule of thumb, not the rule of laws.”
Are you referring to the use of approximation? If so then this seems similar to the point above, the theoretical models of things are only used as a reference point to which you compare a physical measurement, similar to how we compare a measurement of time to the definition of a second, we can compare a set of data to a definition of a function (for instance growth patterns of bacteria that follow exponential trends may not be exactly “2^n” but may be within an acceptable margin of error if approximated to that function using methods such as polynomial interpolation).
[/quote]
I thought about this too, but I assumed that he was talking about how despite the fact that we can and must define units, the dimensions actual physics processes and states never exactly coincide with our measurements, no matter how small the unit. (Of course, unless we define some unit based on those processes or states.)
Thinking about what you said though, there are probably some physical dimensions, say like electric charge, that can in principle be measured exactly. Hence there’s nothing really stopping us from making certain measurements exact.
My understanding of it would be:
a^2 * a^3 = a^5
because you add the power when the integer’s the same. i.e. a.
Therefore,
a^0 * a^2 = a^2
since 0 + 2 = 2
Therefore a^0 must be equal to 1, which we already know.
If we then consider,
0^0 * 0^1 = 0^1 = 0
we know that anything to the power of 1 gives the value of the integer only. i.e. a^1 = a.
Therefore 0^1 = 0, and absolutely anything when multiplied by zero will give an answer of zero. So,
0^0 * 0^1 = 0^0 * 0 = 0
which tells us nothing about 0^0. That is, 0^0 could be absolutely anything! 0, 1, 2 infinity, i, -126 etc. Because we are multiplying by a 0, we will always get an answer of zero, no matter what the values of everything else are.
It’s one of those things studied at university level which deals with logic etc. Sortof like the case of i^i (i is the imaginary component of a value) which appears to give a real value.
[I graduated today with a Bachelor of Science in Physics - I hope I learnt something!]
[quote]huwwaters wrote:
My understanding of it would be:
a^2 * a^3 = a^5
because you add the power when the integer’s the same. i.e. a.
Therefore,
a^0 * a^2 = a^2
since 0 + 2 = 2
Therefore a^0 must be equal to 1, which we already know.
If we then consider,
0^0 * 0^1 = 0^1 = 0
we know that anything to the power of 1 gives the value of the integer only. i.e. a^1 = a.
Therefore 0^1 = 0, and absolutely anything when multiplied by zero will give an answer of zero. So,
0^0 * 0^1 = 0^0 * 0 = 0
which tells us nothing about 0^0. That is, 0^0 could be absolutely anything! 0, 1, 2 infinity, i, -126 etc. Because we are multiplying by a 0, we will always get an answer of zero, no matter what the values of everything else are.
It’s one of those things studied at university level which deals with logic etc. Sortof like the case of i^i (i is the imaginary component of a value) which appears to give a real value.
[I graduated today with a Bachelor of Science in Physics - I hope I learnt something!][/quote]
No, fail.
I wonder how many more people will read the original post, not read the rest of the thread, and then post up something stupid like this.
[quote]stokedporcupine8 wrote:
huwwaters wrote:
My understanding of it would be:
a^2 * a^3 = a^5
because you add the power when the integer’s the same. i.e. a.
Therefore,
a^0 * a^2 = a^2
since 0 + 2 = 2
Therefore a^0 must be equal to 1, which we already know.
If we then consider,
0^0 * 0^1 = 0^1 = 0
we know that anything to the power of 1 gives the value of the integer only. i.e. a^1 = a.
Therefore 0^1 = 0, and absolutely anything when multiplied by zero will give an answer of zero. So,
0^0 * 0^1 = 0^0 * 0 = 0
which tells us nothing about 0^0. That is, 0^0 could be absolutely anything! 0, 1, 2 infinity, i, -126 etc. Because we are multiplying by a 0, we will always get an answer of zero, no matter what the values of everything else are.
It’s one of those things studied at university level which deals with logic etc. Sortof like the case of i^i (i is the imaginary component of a value) which appears to give a real value.
[I graduated today with a Bachelor of Science in Physics - I hope I learnt something!]
No, fail.
I wonder how many more people will read the original post, not read the rest of the thread, and then post up something stupid like this. [/quote]
Seriously? Is that the competency of the average SCIENCE graduate? Geez, that should be high school level, and of course, we wouldn’t be saying shit like that.
EDIT: Oh and yeah, this thread needs to die. 0^0=1.
Deal with it.
[quote]JLu wrote:
Bill Roberts wrote:
debraD wrote:
But it is debatable.
Really, that should have ended the thread, IMO. Seems a quite solid explanation and presentation and – absolutely no disrespect to the posters that followed – no further comment seems to have added anything to the explanation in the link.
Really, this shouldn’t have been posted, IMO. Seems like quite obvious ass kissing and favour seeking and – absolutely no disrespect to you – this comment seems to have ALSO added nothing to the thread.[/quote]
JLu, no disrespect to you, but you are a jackass and – have ALSO added nothing to the thread.
[quote]debraD wrote:
JLu wrote:
Bill Roberts wrote:
debraD wrote:
But it is debatable.
Really, that should have ended the thread, IMO. Seems a quite solid explanation and presentation and – absolutely no disrespect to the posters that followed – no further comment seems to have added anything to the explanation in the link.
Really, this shouldn’t have been posted, IMO. Seems like quite obvious ass kissing and favour seeking and – absolutely no disrespect to you – this comment seems to have ALSO added nothing to the thread.
JLu, no disrespect to you, but you are a jackass and – have ALSO added nothing to the thread.[/quote]
My post wasn’t intended to add anything to the thread, it was intended to mock Bill’s. Understanding joke fail. Oh and no disrespect to you, but you are a bitch. Amidoinitrite?
[quote]JLu wrote:
debraD wrote:
JLu wrote:
Bill Roberts wrote:
debraD wrote:
But it is debatable.
Really, that should have ended the thread, IMO. Seems a quite solid explanation and presentation and – absolutely no disrespect to the posters that followed – no further comment seems to have added anything to the explanation in the link.
Really, this shouldn’t have been posted, IMO. Seems like quite obvious ass kissing and favour seeking and – absolutely no disrespect to you – this comment seems to have ALSO added nothing to the thread.
JLu, no disrespect to you, but you are a jackass and – have ALSO added nothing to the thread.
My post wasn’t intended to add anything to the thread, it was intended to mock Bill’s. Understanding joke fail. Oh and no disrespect to you, but you are a bitch. Amidoinitrite?[/quote]
Where I come from we call that a joke fail.
(Of course, no disrespect to you!)
[quote]stokedporcupine8 wrote:
huwwaters wrote:
My understanding of it would be:
a^2 * a^3 = a^5
because you add the power when the integer’s the same. i.e. a.
Therefore,
a^0 * a^2 = a^2
since 0 + 2 = 2
Therefore a^0 must be equal to 1, which we already know.
If we then consider,
0^0 * 0^1 = 0^1 = 0
we know that anything to the power of 1 gives the value of the integer only. i.e. a^1 = a.
Therefore 0^1 = 0, and absolutely anything when multiplied by zero will give an answer of zero. So,
0^0 * 0^1 = 0^0 * 0 = 0
which tells us nothing about 0^0. That is, 0^0 could be absolutely anything! 0, 1, 2 infinity, i, -126 etc. Because we are multiplying by a 0, we will always get an answer of zero, no matter what the values of everything else are.
It’s one of those things studied at university level which deals with logic etc. Sortof like the case of i^i (i is the imaginary component of a value) which appears to give a real value.
[I graduated today with a Bachelor of Science in Physics - I hope I learnt something!]
No, fail.
I wonder how many more people will read the original post, not read the rest of the thread, and then post up something stupid like this. [/quote]
I did read the rest of the thread and do recognise what you say that science isn’t absolute, it is just a method of finding a model which best describes something that happens using pre-defined concepts (our case - decimal, Newtonian calculus etc.). That model can change if a better method is found, which is the whole basis of peer review, scientific reports etc.
I wrote the above for those who weren’t fortunate enough to go to college. I didn’t assume everyone here had a good understanding of maths but could have a lot of interest in the subject. I think it’s easy enough to follow something like anything multiplied by a zero is zero etc. rather than bringing logs, exponents or other concepts which are usually reserved for university mathematics students.
My little thing simply showed that you couldn’t get a clear answer for 0^0 and was therefore undetermined. Following that you could use other theory to try an obtain a value or start making assumptions like equating it to 1.
I’ll stop now before more people become unnecessarily angry.