the tree

Hi there,

 

To get started with the first few, you'll just need to recall a few basic identities - knowing a^x =e^{ln a x}, the product rule and the quotient rule should get you through those three.

 

Once you've done that, think about the rules you've used and the question with s(t) should look easy.

 

The next one is a little messy so I'd suggest that first you try to work out da/dx for a=a²+ln(x).

 

For the graphing problem, think about range, value at x=0 and limits for both ends of x.

 

For the last bit on that page - just work through it real slow, so long as you remember the basic properties of logarithms then you should be fine.

 

Good luck tho!

From a pure maths perspective you could say that it's a consequence of looking for general rules - the type of relationships that we look for are ones that are symmetrical, invertible etc - which limits the amount of operations that could possibly be used to describe the ones we find.

Taking the limit as h -> 0 is different to just substituting in h=0.

 

You'll need a better idea of limits before trying to work your way through that proof.

You just made a tiny mistake, you should be looking at:

 

[math]\lim_{h \to 0} \frac{(x+h)^2 - x^2}{h}[/math]

 

you'll find it works out easily.

ok so i want to know if there is an easier way to figure out how many times you would have to double a number before getting to certain number. (other then going 2x2x2x2x2x2x2

 

question two lets say we take the number 1080 is there a way to figure out how many times it had been doubled assuming the start point is 1

That would be what logarithms are for. If y=2^x then log₂(y)=x.

 

In the case of your example, log₂(1080)=10.077...

 

So we know that it's not 1 doubled a whole number of times. The best we can say at that point is 2¹⁰<1080<2¹¹.

 

A little further investigation will tell you that 1080=2¹⁰+56.

 

If your calculator cannot do base 2 logarithms then you'll have to use the natural logarithm ( ln or log_e ) and to do that you'll need to know that log_b(x)=ln(x)/ln(b).

 

what if the starting number was 4 any way to figure that out besides the long way

Well I think since 4=2² you might be able to work that out.

Having offspring is the evolutionary equivalent of living forever.

Why not override evolution and eliminate the stress of offspring while continuing to live your own life for as long as science allows?

Because evolution's solution is a lot better than anything we've ever come up with. The problem is that things will always fall apart eventually, entropy increases, nothing should last forever and that's sort of built into the universe. We can patch things up or whatever. But things that make new things, with adaptation to a varying environment, we haven't found a better solution.

How do you conclude about the value 'i'?

Because it is a value that doesn't exist.

That isn't how it works in the slightest.

 

2. the belief that the symbol "0" is a number - when it isn't . It's the absence of a number. Recall that the symbol was invented as a place-marker[...]And so mathematicians try to treat it as a number, when it isn't. And that's why the mathematicians get confused, and see problems and paradoxes, when really there aren't any.

• 0 is a number.
  • It doesn't fall under the range of the domain of the division function.
  • But it's still a number.

  [*]You're correct in that there are no problems or paradoxes.[*]I really doubt any mathematicians are confused by this.

I'd sort of given up the non geometric view of pi, since connector seemed so obsessed with the idea that circles were a requirement in some way.

 

Also he's saying that sqrt(2) doesn't exist.

 

What the hell.

Nah that's fine I'll take it.

 

I guess we can throw out the numbers 5, 17, 130.2 and 9, while we're at it.

But in real Nos zero is not defined as you mention in your second line of proof.

0 is defined as the number with these two properties:

• x+0=x
• x*0=0

So in fact, it is.

For example, what do you mean the square root of 2? I've never ever found a number that can multiply by itself to equal 2, have you? Please share. As far as I know there is no square root of 2, only something really really close. Really close is an approximation just like pi.

Are you seriously suggesting that just because a number doesn't have a finite decimal expansion, that means it doesn't exist?

• Okay we all know that you can't draw a perfect circle in the physical realm, no-one is contending that.
  
• But we're talking about pi as a mathematical object, not a physical one.
  
• A mathematical object that has plenty definitions that don't mention a single geometric concept, let alone circles.
  
• If you're trying calculate pi then you're doing a calculation which is different than a measurement in that it's not the same thing
  
• The proof that pi is irrational is actually a little bit complicated
  
• It's not just "rah rah smooth surfaces approximate unsmooth ones"
  
• That's not what a proof is
  
• Or an argument
  
• Or really anything that has any place in mathematics
  

 

As an aside, the square root of two is also irrational and can fairly easily be depicted with a finite amount of straight lines, how does that contend?

The tree, by realizing that using a formula for a shape with infinite polygonal sides you will get an infinite 'estimate', we can learn valuable things such as:

Pi will go on forever

Pi will never have a pattern

How do these follow?

For that matter it'd be trivial to contrive a smooth curve with an integer length, even though it's length actually would be regarded as the sum of infinite straight lines.

True circles are an impossibility, why would we expect them to work out on paper?

We don't expect them to: they do.

-0 = -1*0 by definition of "-"

-1*0 = 0 by definition of "0"

-0 = 0 by transitive property of "="

Q.E.D.

The reason pi is infinite is because people forgot what pi is actually describing

The period of e^ix? A consequence of the axioms of euclidean geometry?

a lie.

Hmm?

from 2d to circles to 3d spheres, nothing has a perfectly smooth or round surface.

So?

If you take a measurement of something such as a round lid....

Then you wouldn't be doing mathematics would you?

You're welcome.

Prey tell, for what?

 

Seriously. Most real numbers have an infinite decimal expansion. It's not a big deal and you don't need to make up ridiculous explanations for it.

There is only one person here dumb enough to call any such nonsense a "proof".

I reckon if you really trawled through the forums then you'd find a handful.

Say the pitchers were already lined up waiting to be assigned a catcher: the first can be put with one of 5 catchers, the second can be put with one of 4 remaining catchers, the third with one of 3 remaining catchers...

 

How might you factor all those possibilities in!

That was the intention yes.

I'm willing to bet it's along the lines of

 

x = x

x^2 = x*x

x^2 - x^2 = x*x - x^2

(x + x)(x - x) = x(x - x)

x + x = x

2x = x

x != x

 

which I think we can all agree is utter rubbish. Do we really need to pursue that any further?

How can the offspring of "Cuban Immigrants", dare to speak like a politician?

Because he was elected to do so by the people who it is his job to represent. That's how politics works.

Well that's boring.

what

But what is the purpose of contriving a new numeral system? There are already plenty.

Has someone been watching too much Stargate?

 

Probably not you can't have too much Stargate.

can i buy a new one and use it on the old one

I don't think they sell just the vacuum chambers by themselves.

Though if you were to able to assemble one, presumably the filament would still be undamaged enough to work?