This article gives the cardinal number of the set of all binary numbers by counting its elements, analyses the consequences of the found value and discusses Cantor’s diagonal argument, power set and the continuum hypothesis.
1. Counting the fractional binary numbers
2. Fractional binary numbers on the real line
3. Countability of BF
4. Set of all binary numbers, B
5. On Cantor’s diagonal argument
6. On Cantor’s theorem
7. On infinite digital expansion of irrational number
8. On the continuum hypothesis

Please read the article at
Cardinality of the set of binary-expressed real numbers
PDF http://pengkuanonmaths.blogspot.com/2015/12/cardinality-of-set-of-binary-expressed.html
or
Word https://www.academia.edu/19403597/Cardinality_of_the_set_of_binary-expressed_real_numbers

This experiment shows the magnetic force on a coil exerted by the magnetic field of a long solenoid (1.95 m, 6.4 foot) that should be zero.

Please read the article at
A 1.95 m long solenoid exerting Aharonov–Bohm force on a coil
http://pengkuanem.blogspot.com/2015/10/a-195-m-long-solenoid-exerting.html
or
https://www.academia.edu/17214485/A_1.95_m_long_solenoid_exerting_Aharonov_Bohm_force_on_a_coil

The magnetic field of the earth can rotate a flat coil in its plane. This is explained in Earth’s magnetic field and parallel action. Will a disc magnet rotate a flat coil the same way? The magnetic field of a disc magnet is central symmetric and the field lines are contained in median planes (See Figure 1). If a flat coil is coplanar with a median plane, the Lorentz forces on the currents will be perpendicular to the plane of the coil. So, Lorentz force could not rotate the flat coil in its plane. But in my experiment the coil rotates.

Please read the article at
Disc magnet parallel action experiment
http://pengkuanem.blogspot.com/2015/06/disc-magnet-parallel-action-experiment.html
or Disc magnet parallel action experiment (video included)
https://www.academia.edu/13033082/Disc_magnet_parallel_action_experiment_video_included_

Earth’s magnetic field and parallel action

The magnetic field of the earth is uniform on its surface. The resultant Lorentz force a uniform magnetic field exerts on a coil of any shape is zero. The torque perpendicular to a flat coil is also zero. So, a current carrying coil in the magnetic field of the earth should stay immobile. However, my experiment shows that the test coil rotates in its plane. See the video of this experiment: http://youtu.be/JKMG8jY1RRg

Please read the article at
Earth’s magnetic field and parallel action
http://pengkuanem.blogspot.com/2015/06/earths-magnetic-field-and-parallel.html
or Earth’s magnetic field and parallel action (video included)
https://www.academia.edu/12926460/Earth_s_magnetic_field_and_parallel_action_video_included_

In “Q: Parallel action with a solenoid” I have asked a question: the magnetic field of a long solenoid being zero, will it make a coil rotate in its plan? This experiment will investigate the parallel action of a long solenoid. I have done this experiment and here is my result.

Please read the article at
Solenoid parallel action experiment
http://pengkuanem.blogspot.com/2015/06/solenoid-parallel-action-experiment.html
or Solenoid parallel action experiment with video included
https://www.academia.edu/12722675/Solenoid_parallel_action_experiment_with_video_included

According to my corrected magnetic force law, parallel currents attract each other and anti-parallel currents repel each other, see Theory about parallel action experiment. So, for the rectangular coil near the solenoid in Figure 1, the upper current is parallel to that in the front side of the solenoid and the lower current is anti-parallel. So, there would be a torque created on the coil and the coil should rotate.

However, the magnetic field outside a solenoid is zero and cannot act any force on a current. Moreover, there cannot be force parallel to current for classical theory.

So, If I do this experiment, will the coil rotate or not?

Please read the article at
Q: Parallel action with a solenoid
http://pengkuanem.blogspot.com/2015/05/q-parallel-action-with-solenoid.html
or
https://www.academia.edu/12426677/Q_Parallel_action_with_a_solenoid

Nearly two years ago I proposed a CRT experiment to test the magnetic field of a solenoid, see Non-Lorentzian Magnetic force and Aharonov-Bohm effect in CRT, Blogspot, Word published June-27-2013. Since its consequence is great (see Consequences of macroscopic Aharonov-Bohm effect, Blogspot, word), I thought glory-searching physicists would rush on this simple experiment. But until now no one has dared to take the trophy and I have finally decided to carry it out myself. The result is as I predicted.

Please read the article at
Aharonov–Bohm effect in CRT experiment
http://pengkuanem.blogspot.com/2015/04/aharonovbohm-effect-in-crt-experiment.html

or
https://www.academia.edu/12052541/Aharonov_Bohm_effect_in_CRT_experiment_Video_included_

pdf
or word

The Induced conductor net problem could be solved if we can determine the induced voltage in part of the circuit. But is it possible that a voltage exist in no-loop wire? Let us see what the induced voltage is in a circular loop formed with 4 segments separated by resistors

Please read the article at
Non-loop induced voltage problem
http://pengkuanem.blogspot.com/2015/03/non-loop-induced-voltage-problem.html

or
https://www.academia.edu/11701041/Non-loop_induced_voltage_problem

pdf or word

My article Coil and resistor induction paradox shows that the potential energy of electrons in an induced coil is not correctly described by Faraday’s law. This is illustrated by Figure 1 in which a circular circuit with a resistor A is induced in a magnetic field; the resistance of the wire P is negligible. The inconsistency is that the electric field in the conductor wire P is zero and the moving electrons cannot collect energy. The present article exposes another problem: finding the potential in induced circuit with multiple resistor and branches.

Please read the article at
Induced conductor net problem
http://pengkuanem.blogspot.com/2015/03/induced-conductor-net-problem.html

or
https://www.academia.edu/11470407/Induced_conductor_net_problem

pdf or word

In my article Faraday’s Law Paradox, I have explained that in a magnetically induced coil the line integral of electric field is paradoxically zero in contraction with Faraday’s law. This paradox has aroused a long discussion which also reveals that the air gap between the coil’s terminals confused the understanding of the paradox. The closed coil below makes this paradox sharper. I will give my solution to this paradox.

Please read the article at

Coil and resistor induction paradox pdf or word

http://pengkuanem.blogspot.com/2015/02/coil-and-resistor-induction-paradox.html

or
https://www.academia.edu/11113117/Coil_and_resistor_induction_paradox