Recent content by ato

No, its wrong to use of addition of vector law to add to vectors from different reference frame. For example consider two frames with same origin at O' but with different oriantitions. According to ##r_{OO'} = r_{OP} + r_{PO'}##, the ##r_{OO'}## for each frame would coinsides. But they should...

\vec{r}_a is a positional vector from reference frame a. What is the position of same point from reference frame b ? If required, assume position of origin of frame a is \vec{m} and unit point (i.e. \langle 1,1,1\rangle_a ) is \vec{n} from reference frame b. I am studying Kleppner and Kolenkow...

got it, thanks

i was following alright until this. do you mean this is correct, ##P(x)\textrm{ is unprovable for }x\in N\Rightarrow x\notin N## but then P(x) would never be unprovable (hence redundant) because ##P(x)## is true for ##x\in N##. why would x∈N assumed as condition ? would not this require N to be...

ok, its page 15 on Week 1: Introduction to analysis; the natural number system; induction; the integers; the rationals . the notes has mentioned four axioms to construct the set , 1. 0 is natural number 2. n is natural number ⇒ n++ is natural number 3. n is natural number ⇒ n++ ≠ 0 4. (n,m are...

i am studying real analysis from terence tao lecture notes for analysis I. http://www.math.ucla.edu/~tao/resource/general/131ah.1.03w/ from what i understand , property is just like any other statement. for example P(0.5) is P(0) with the 0s replaced with 0.5 . so the notes says (assumes ?)...

P → Q is defined as if P → Q is True then ( if P is True then Q is True . ) is true. if ( P is True. Q is True. ) then P → Q is True. if ( P is False. Q is True. ) then P → Q is True if ( P is False. Q is False. ) then P → Q is True if ( P is True. Q is False. ) then P → Q is False...

##E## does exist, ##\{(a,a^{2},2a)|a\in R\}\subset R^3## we konw -2 exist right. should not -{0,1} exists. ##3 - 2 = 1## ##\{ 0,1,2 \} - \{ 0,1 \} = \{ 2 \} \neq 1## is not that a paradox/contradiction. thank you

yes the question did ask for ##\frac{d}{dt}f(x(t),y(t),z(t))## . the theoram used to solve is ##\frac{\partial f(x,y,z)}{\partial t}=\frac{\partial f(x,y,z)}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial f(x,y,z)}{\partial y}\frac{\partial y}{\partial t}+\frac{\partial...

lets consider a textbook question here is my solution : 1. ##f(x,y,z) = x^{2} + y^{2} + z^{2}=x^{2}+x^{4}+4x^{2}=x^{4}+5x^{2}## 2. ##\Rightarrow f(x,y,z)=x^{4}+5x^{2}## 3. ##\Rightarrow\frac{\partial}{\partial x}f(x,y,z)=\frac{\partial}{\partial x}(x^{4}+5x^{2})## 4...

reading the definition (given in the link), i admit following things 1. a function is a set , where each element is an orderd pair and composed of two elements taken from two sets. the vice versa may or may not be true. (f is still a variable though). but you also say is not that...

let me add parameter in the confusing concepts list. assuming for a function,all parameters are independent. then you can't say because we don't know if x,y are independent of each other. in fact i added x = y so its false that x and y are parameters. may be x or y is a parameter but both...

still waiting for a reply, guys ! so, I am going to bump the thread, just this once .

how can both x and y be independent variables if both depend on some other variable ? would not the value of x (for example) imply the value of y ? if x and y are truly independent would not $$\frac{\partial f(x,y)}{\partial x}=\frac{df(x,y)}{dx}$$ does it matter ? thank you

i am having a hard time understanding partial derivative for function of dependent variables. for example let's consider $$z=x+y$$ so by usual steps that are mentioned on e.g wikipedia etc. $$\frac{\partial}{\partial x}z=1$$ but what if its also true that $$y=x$$ (or in other words...