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1. Prove that spec of root 2 contains infinitely many powers of 2.

I've been thinking about it but I can't seem to move ahead. sqrt(2) is irrational. It's binary representation has no pattern. It would look like 1.0110101000001001111... and multiplying by 2^n would left-shift it n times. Taking floor of this irrational number loses a portion of the number...
2. Prove that spec of root 2 contains infinitely many powers of 2.

Here, it means Spec√2= {⌊k√2⌋ : k≥0}
3. Prove that spec of root 2 contains infinitely many powers of 2.

Spec of root 2 is that set of elements floor(k * (root 2)) ; k >= 0 . I have no idea of how I can prove the statement in the question. Prove that spec of root 2 contains infinitely many powers of 2. I need ideas on how to proceed. Thank you
4. What inside the band gap?

Okay,thank you all.
5. What inside the band gap?

but those frequencies are integral multiples of some fundamental frequency. There are no bands. Here every possible energy in a band is possible,but energies between 2 bands isn't possible. This,I don't understand.
6. E-k diagram what is k?

In the E-k diagrams for a semiconductor material,what exactly is k? I have read that it is a propagation constant,a wave vector. But does movement in the semiconductor material represent corresponding changes in k? I mean to ask if changes in k represent the physical movement in the...
7. What inside the band gap?

I am reading about solid state electronics(semiconductors). I've read that when atoms of many many atoms are brought close each other,as in a solid, the energy levels of energy states of different atoms get split up into different closely lying energy states collectively forming a band...
8. Hall Effect

We have an experiment on Hall Effect,in which we place a semiconductor material in the middle of a 2 poles of a magnet exactly in the middle so that a distance of 1 cm exists between the poles. Questions: 1.Why is a semiconductor placed?Will it make any difference with a metal? 2.Why a 1 cm...
9. Magnetism to test for movement?

Oh Thank You pervect:) I am sorry for the late reply,I didn't have easy access to a computer.
10. Magnetism to test for movement?

ghwellsjr,I didn't completely understand that. pervect, Thank You for your explanation. But we have a formula of electrostatic force between two charges don't we? Are you saying that the constants in that change with the motion.(pi and epsilon?) I mean,doesn't the guy in motion have the...
11. Magnetism to test for movement?

Now suppose we were to find the actual magnetic force. Then would it not fetch us an absolute velocity? What came out of them?
12. Magnetism to test for movement?

They say it is impossible to know whether you're moving at constant velocity or at rest unless you look outside. How about this:(no gravity please) I take two known charges and hold them at a distance one above the other. They repel.That is l I know. Someone else outside says,that the...
13. Job description in computers and electronics

okay,where may find out all these?
14. Job description in computers and electronics

Hi. I am now to choose what I must study for engineering. So,I wanted some help.Everyone says "you must take what you like and what you will enjoy doing and what will make your job enjoyable". But,I don't know what I'll learn in engineering and what job I'll have to do. (I have to pick among...
15. Plane mirrors (multiple)

Homework Statement How many images of a symmetrically placed object will be formed if 2 plane mirrors are fitted on ADJACENT walls of a room and another one on the top(roof)? (mirrors are big) 2. The attempt at a solution According to me,9. because,3 direct images of the object are...
16. Capacitor discharge

Oh yes. Dumb of me. It is the electrons that flow through the circuit and reach the positive plate and neutralize the positive charge on the plate. Thanks !!!
17. Capacitor discharge

Homework Statement A fully charged capacitor is connected in a closed circuit with nothing else in the circuit. So the capacitor starts discharging.At a certain instant of time the charge on the capacitor is reducing at the rate of 5 micro coulomb per second(dq/dt =5 μC per s). What is the...
18. Question regarding onto function

Hi. I know what an onto function is. I found this statement on a problem: f(x) is a function from a set Z onto itself. Now does this mean that f(x) is an "onto" function or is the word used just like that(like an english word)? What if it was: f(x) is a function from a set Z into itself...
19. Root of square of something

Consider this function: (x^2)^0.5 My text book considers this to be |x| (modulus of x). Is it correct? x^2 gives a positive quantity.On taking square root of that,we'll get either -x or +x. So why modulus? Also, (x^0.5)^2 This is modulus isn't it? Thank You
20. Physics homework on springs

Okay then.Thank you
21. Physics homework on springs

Okay,I got the case when same force acts at both ends. How about this?I take a spring in my hand vertically,and pull the upper part by 5N amd the lower part with the other hand by 10 N. As you said: "The tension in a string or a spring is the force that it exerts at each end." now no matter by...
22. Physics homework on springs

Okay,then consider the 1 st situation I put up with both the masses same say 'm'. Now,let extension of spring be 'x'. As you said,the spring pulls both the blocks with the same force kx and this force keeps each block in equilibrium.That makes kx=mg so x=mg/k. But,considering tensions,the...
23. Physics homework on springs

Please consider the following case: Spring connected at both ends by some masses.Everything is ideal. Find the extension of the spring. http://img101.imageshack.us/i/unledpi.jpg/ http://img101.imageshack.us/i/unledpi.jpg/ My big question is ....if the spring extends by a length say...
24. Linear speed rolling

Okay.Thank You Doc Al.I understood.:smile:
25. Linear speed rolling

Yes,nothing got to do with horizontal,I'm very sorry. Isn't the instantaneous axis the one passing through the centre of the rim,into the plane of paper (of my attached diagram)?
26. Linear speed rolling

Here it is word for word: A point on the rim of the wheel of radius R under pure rolling has absolute ground speed of (v root 2) or v*(2)^(1/2).the angular speed of rotation is ω. It is 'x' distance away from the instantaneous axis .Find x. yes I made some errors while writing it here,BUT what...
27. Linear speed rolling

Okay. I took the whole vector and added it.I get the answer as R.It seems right as the particle at the side will have a velocity v upward and v sideways. But still,the answer is supposed to be R root 2,which confuses me even further,as the radius of the rim is only R!!Am I missing something big?
28. Linear speed rolling

I tried it with your method like this. As seen from the diagram I uploaded, the horizontal component of Rω (speed of particle)is taken in terms of theta. Then v + Rω sin (theta) =v*(2)^(1/2). I found theta and then found the required distance. But that doesn't match with the answer given...
29. Linear speed rolling

Homework Statement A point on the rim of the wheel of radius R under pure rolling has absolute ground speed of (v root 2) or v*(2)^(1/2).the angular speed of rotation is ω. At what horizontal distance from the instantaneous axis of the rim is the particle located? Homework...
30. Question about law of reflection

Hey. So you're saying that we must keep an observer near the mirror and then view the object,and find object distance and blindly use u=v? Are you sure? I have heard people argue that that can't be done as the rays after reflection will further get refracted at the slab air interface and this...