triclino

This is my main objection , how do we prove that v is perpendicular to r

Thanks ,but you have to explain each step because i am a bit confused: How do you get : [math] {\mathbf{v}} = v (-sin\theta\hat{\mathbf{x}} + cos\theta\hat{\mathbf{y}}) [/math]

proof without using geometry at all ,but only vector analysis. In the proof that i read in most books they use the properties of similar triangles . In proving that r.r=r^2 you can do that without using the fact that cosθ =1

I think you would enjoy the high school problem in post #7.

D.H the word is foundations . Do you know which are the foundations of mathematics ?? What is your definition of mathematical proof?? Do you perhaps know any efficient way of checking why a mathematical proof is correct or not?? Here is a high school mathematical proof (to start with easy one). Prove: |x|<y proof: |x|<y <=> [math]|x|^2<y^2\Longleftrightarrow x^2-y^2 <0[/math] <=> (x+y)(x-y)<0 <=> {[(x-y)<0 and (x+y)>0] or [(x-y)>0 and (x+y)<0]}. IF [(x-y)<0 and (x+y)>0] <=> x<y and x>-y <=> -y<x<y.................1 IF [(x-y)>0 and (x+y)<0] <=> x>y and x<-y...................................2 From (1) and (2) we conclude that : |x|<y <=> -y<x<y Is that proof correct or not???

In most physics books ( even the University ones) i looked at, they use geometry to derive that the acceleration is [math]\frac{v^2}{r}[/math],where v is the constant speed and r is the radius (magnittute of the position vector r) of the motion. Can we not use pure vector analysis to derive the above fact??

Why ,when x=2a and y=2b ,then x+y=2a+2b?.What is the axiom ,theorem or definition supporting that statement??. From how many arguments your proof consists of?? Can you isolate each argument??. For example can you say : Argument No 1 : state the argument Argument No 2: state the argument Argument No 3 : state the argument .............e.t.c........e.t.c Merged post follows: Consecutive posts merged Yes this the right question ,why x=2a and y=2b ,what is the axiom ,theorem or definition supporting those statements. The answer here is the following: Definition: for all ,x : x is even => there exists integer ,a such that x=2a Or in quantifier notation : [math]\forall x[/math][ x is even[math]\Longrightarrow\exists a( a\in Z\wedge x=2a)][/math]. The final statement x=2a ,y=2b ,where a,b are integers is concluded in the following way: step 1 : Assume ,x,y to be even step 2 : bring in the above definition of even Nos: [math]\forall x[/math][ x is even[math]\Longrightarrow\exists a( a\in Z\wedge x=2a)][/math] step 3: What do you think step 3 should be???

Here is an alternative proof: Let A be the area of triangle x ,the height z the side of the triangle y the base of the triangle And , θ the angle between the height ,x and the side z Now all the above except , θ ,change with time . We also know dz/dt . So if you can express A in term of ,θ and z ,then the calculation of dA/dt will be an easy matter. So,the area of the triangle is: A = (y.x)/2.........................................................................................1 But : sinθ = [math]\frac{\frac{y}{2}}{z} = \frac{y}{2z}\Longrightarrow[/math] 2zsinθ = y.........................................................................................2 cosθ = [math]\frac{x}{z}\Longrightarrow[/math] zcosθ = x......................................................................................................3 And substituting (2) and (3) into (1) we have: A= sinθcosθ[math] z^2[/math] Now we can differentiate w.r.t time ,t. Thus : [math]\frac{dA}{dt}[/math] = sinθcosθ[math]\frac{d(z^2)}{dt}[/math]=2zsinθcosθ[math]\frac{dz}{dt}[/math],but since dz/dt = 2ft/min and zcosθ =x we have that: [math]\frac{dA}{dt}[/math]= 4xsinθ (ft\min). And since we want the rate when x=8ft ,then we have: [math]\frac{dA}{dt}[/math] = 32sinθ ([math]\frac{ft^2}{min}[/math]). Where θ =arctan[math]\frac{\frac{19}{2}}{8}[/math],if when x=8ft ,y=19ft

Tacobell The only thing that does change with time is the angle, θ between the side of the triangle and its height. So if you can express the area of the triangle in terms of this angle and one of its sides ,then very easily you will find the: dA/dt of the triangle,because you know the d(one side of the triangle)/dt = 2ft/min

Can you find anywhere such a theorem?

Now if this is not another pack of mathematical nonsenses what is it then? You keep on writing non existing theorems and conclusions ,by simply imagining them.

Yes you can escape by writing nonsenses because the moderators of this forum perhaps are not capable of detecting such unfounded mathematical nonsenses that you keep on writing.

. I see you have a problem in reading : The section under properties it says that: if the interval on which A continuous function f is defined is COMPACT then the function is uniformly continuous. Is the interval (0,[math]\infty[/math]) on which f is defined COMPACT???

So, how does the definition of a bounded sequence help to prove that the sequence has a limit . Read the question again ,it says to prove that the sequence has a limit by using the theorem (axiom) of nested intervals

You mean that: IF [math]lim_{y\to y_{o}}(lim_{x\to x_{o}}f(x,y))=f(x_{o},y_{o})=x_{o}.y_{o}[/math]..................... THEN [math] lim_{(x.y)\to(x_{o},y_{o})}f(x,y) =f(x_{o},y_{o})=x_{o}.y_{o}[/math]???

On what theorem or axiom you base such a conclusion.

It seams to me that you do not know the definition of uniform continuity. As for the theorem you stated it exists nowhere in the whole of cosmos. Anyway if you still insist on the validity of your theorem ,then give a proof.

How can you prove that left and right limits are equal?? How do you know that f(x,y) is continuous at ([math]x_{o},y_{o}[/math]),without proving it

.. That is the definition of a function being continuous on an interval and not the definition of a function being uniformly continuous over an interval

Your conclusion is based on what definition or theorem?

Can you give an example to justify your definition? Hence to produce a proof consisting of "logical arguments" where those arguments can be isolated and examined for there validity in an indisputable and clear way?? By the way in logic we do not have "logical arguments" ,but valid or not valid arguments

I think every mathematical forum at the very beginning of its existence should produce a definition of the mathematical proof and then according to that definition every mathematical proof should be written down. Also a check process should be mention ,hence to avoid useless duals between the members of the forum whether a proof is correct or not. I think the above should be stipulated as the basic rules of each and every mathematical forum

Is a sequence increasing or decreasing

That is not a proof is there??

How do we -prove that: The axiom (theorem ) of the sequence of the nested interval in real Nos implies that every monotone sequence in real nos ,bounded from above, has a limit