Correct. Even the very definition of a "straight" line gets bent out of shape near the speed of light. A straight line is defined as the path that light travels.
If you do a boost (something that changes the speed of your reference frame) this isn't true. But it remains true that $p^2=(E/c)^2-(\vec{p})^2$ is left unchanged by such a transformation.
Some time after the rocket launches, the person on earth tosses a ball in the air and catches it at the same height in time T.
From their perspective, there was no separation in space between the two events. So $\Delta t=T, \Delta x=0$, and the spacetime interval is $cT$.
From the perspective of the person on the spaceship, though, Earth would have moved a certain distance $a$ farther away in the time that the ball rose and fell.
Semiclassical do you know of any good tutorials for convolution, I dont know what to do with the bounds of integration here $f * f * f$ where $f$ is the characteristic function of the unit inverval
Anyway, it's definitely a good idea to google for what settings you can/should disable. By default, you're pretty much sending Microsoft everything you do.
hi i got something im now sure about . if $H: X \times X \to Y $ is continuous and i define $h : X \to Y$ by $h(x) = H(x,x)$ is it follows that $h$ is also continuous? i think yes but not sure how to show it.
i have $f,g :I \to Y$ that homotopic, so there is $H : I \times I \to Y$ s.t bla bla. now i define $h: I \to Y$ by $h(x) = H(x,x)$ , i just need to say $h$ is continuous
It's fine if you want to say that it is continuous as a function with domain the diagonal, you need to justify it if you want to think about it as a function $X\to Y$
that's cofinality. For an ordinal $\kappa$ $\text{cof}(\kappa)$ is the order type of the smallest cofinal subset of $\kappa$. Where a subset $Y$ of an ordered set $X$ is called cofinal if for every $x\in X$ there is an $y\in Y$ with $y>x$
I wrongly remembered the definition. You were right all along.
but I'm also right all along... you're just choosing a final segment of the ordinal, for countable ordinals.
Hence my confusion with $\aleph_\omega$, since the set chosen isn't the final segment...
You have five cases. $x<a<b<c<d$, or $x$ is between $a$ and $b$ (which I did above), or $x$ is between $b$ and $c$, or between $c$ and $d$, or after $d$.
The left side is:
$X^{(\mu \nu )}Y_{\mu \nu }=\frac{1}{2}\left (X^{\mu \nu }+X^{ \nu \mu} \right )Y_{\mu \nu }$
But the right side does not give me the same. Can you help me please?
> The cofinality of any ordinal α is a regular ordinal, i.e. the cofinality of the cofinality of α is the same as the cofinality of α. So the cofinality operation is idempotent.
@AkivaWeinberger First why are you always putting a $ in front of a variable ? Well if x is for example smaller than a its also smaller than all others variables and the whole product is positive
@AkivaWeinberger OK i got it now, but back to my question. if x is for example smaller than a its smaller than all the other vars and hence the whole product is negative
The left side is:
$X^{(\mu \nu )}Y_{\mu \nu }=\frac{1}{2}\left (X^{\mu \nu }+X^{ \nu \mu} \right )Y_{\mu \nu }$
But the right side does not give me the same. Can you help me please?
