mathematic

Since the numbers in the interval are uncountable, no (countable) sequence can generate all the numbers in the interval.

Think of a block of wood. On dry land it has a weight. But on water it floats, so its "weight" is zero.

This is not completely true. There are matriarchal societies (in Papua among other places) today.

Rather than L'Hopital's, one can take the first few terms of \(sin(x)=x-x^3/3! +x^5/5!+...\) to get -1/3!, as \(x\to 0\).

How are x_i related?

The whole universe is a simulation on my computer.

The value of pi is not something people decide on. It simply comes from its definition.

Pi is transcendental, phi is algebraic. It is very hard to see a connection.

3. Looks strange. Why purple?

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0110 1010=0x2^7+1x2^6+1x2^5+0x2^4+1x2^3+0x2^2+1x2^1+0x2^0

Hooray!!!!

It looks to me the first step for two parallel lines is pick a point on one line and then find the distance to the other line. An alternative (without calculus) to the solution I had described is to set up the general form of a line perpendicular to the given line and then adjust one parameter to make it pass through the given point.

The problem you have is different from the problem in the post (2.10) - distance between parallel lines.

First equation is distance between given point and any point on any line. Next replace y by function of x for given line. Use calculus to get minimum distance and get particular point on line that is minimum.

9.\( d^2=(x-6)^2+(y-2)^2\), where \(y=6x+3\). Or \(d^2=(x-6)^2+(6x+1)^2.\) To minimize calculate derivative and set to 0. \(2(x-6)+12(6x+1)=0\) leading to x=0 and y=3 or \(d^2=37\). 10. Statement is incomplete.

It stops contamination. However radiation from the contents will be dangerous. That is why permanent safe storage is a problem.

The major problem is that radioactive materials (fallout) settle on soil, etc. For soil, the material can leech into the ground, so surface cleaning would not be enough. These radioactive materials emit radiation which ca be very damaging to living things.

It looks like w=h(t).

While I am typing something fairly lengthy, occasionally a message pops up asking if I want to go into some mode, where I don't type. When I see it, my answer is always no However on occasion I am busy typing without looking at the screen. If this message pops up and I don't check no, it assumes a yes answer and locks the keyboard. How can I get the keyboard back? Whenever it happens, the only recourse I know about is do a restart, which is a nuisance.

What was the area of research at these labs? Could the Swiss lab have had smarter people?

Reference cannot be accessed.

Usually 1/infinity is treated as zero, not undefined.

Division by 0 is illegal, so there is no such number!

The description only makes sense for small volume, where everything is in close proximity. .. Extreme counterexample - the ocean