Pauli's philosophical investigations addressed core and fundamental issues, such as the nature of scientific observation and the ontology of scientific theories. For the cutting-edge physicist that Pauli was, a natural extension to these questions would have been: What is mathematics? What is the ...
premises. Anargument is said to be valid when we can deduce (work out) the conclusionfrom the premises. Such an argument is known as a deductive argument. Ina deductive argument, if the premises are true, the conclusion must also betrue. But being able to deduce the conclusion from the ...
Chaos theory is a mathematical concept that explains that it is possible to get random results from normal equations. The main precept behind this theory is the underlying notion of small occurrences significantly affecting the outcomes of seemingly unrelated events. Chaos theory is also referred to ...
This is fairly well known, but it took a little effort for me to locate the required arguments, so I am recording the calculations here. The first observation is that every unit quaternion induces a unit tangent vector on the unit sphere , located at ; the third unit vector is then ...
Counting a mixed collection of coins whose sum is less than or equal to one dollar; solving real-world and mathematical problems within one dollar involving quarters, dimes, nickels, and pennies, the cent symbol appropriately. i) Create a bingo board with amounts less than $1 (e....
Frank Drake is mostly known for developing the Drake equation(方程式),which is a mathematical equation that was developed to estimate the number of detectable alien civilizations residing in the Milky Way.Drake equation takes many things into consideration from the rate of star ...
Mode is most useful as a measure of central tendency when examining categorical data, such as models of cars or flavors ofsoda, for which a mathematical average median value based on ordering can not be calculated. Examples of the Mode ...
Ergodicity is one of the most important concepts in statistics. Ergodicity is a mathematical concept suggesting that a point of a moving system will eventually visit all parts of the space the system moves in. On the opposite side, non-ergodic means that a system doesn’t visit all the possi...
The Malthusian growth model is a mathematical equation for population growth. It holds that the rate of growth is proportionate to the current population. This is functionally equivalent to exponential growth, where the size of the population doubles at predictable intervals. ...
So the main problem is to get control on such infinite sumsets. Here we use a very simple observation: Proposition 1 (Iterative approximation) Let be a Banach space, let be sets with each contained in the ball of radius around the origin for some with convergent, so that the infinite su...