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Mathematical Analysis
Mathematical analysis is, simply put, the study of limits and how they can be manipulated. Starting with an exhaustive study of sets, mathematical analysis then continues on to the rigorous development of calculus, differential equations, model theory, and topology. Topics including real and complex analysis, differential equations and vector calculus can be discussed in this category.
2,575 Questions
Does an equation tell the whole story?
No. An equation can remain unanswered, it may be incomplete and it may be inaccurate.
What is the definition of line segment?
a closed interval corresponding to a finte portion of an infinite line.They are labeled with two letters.
A transform is not inherently a compression; rather, it is a mathematical operation that converts data from one representation to another, often for analysis or processing. Compression specifically refers to reducing the size of data to save space or bandwidth, while transforms can be used for various purposes, including enhancing, filtering, or compressing data. However, some transforms, like the Discrete Cosine Transform (DCT), can facilitate compression by reorganizing data to exploit redundancy.
What is 40 square feet by 80 square feet?
It is a hypercube in 4-dimensional space with an area of 3200 quartic feet.
How much does a mass spectrometer cost?
Its hard to find prices since you almost always need a quote to see the cost from a company. It also depends on what type of MS you are looking at and there are even MS/MS instruments (its basically what it looks like - two mass specs together).
Basically the price range will start at 100k
100,000 - quadrupole MS
100,000 - ion trap MS
300,000-500,000 - quadrupole-Time-of-flight MS/MS or TOF-TOF MS/MS
800,000 - Fourier transform MS
There are other types out there which could increase the price, like automated systems and expensive ionization techniques
Does any number divided by zero equal infinity and if not why not?
A number divided by zero is held to not equal infinity, or anything else, and this is purely convention.
In reality, as zero represents "nothing", you could easily fit an infinite amount of "nothing" into a "something".
One can see this by taking "10" as the "something".
Now ten can go into that "10" one time. A perfect fit, so to speak.
Five can go into that "10" two times. Why? Because five is half of ten, and two halfs go into a whole two times.
One can go into that "10" ten times. Why? Because one is 1/10th of ten, and a tenth goes into a thing ten times.
Now from this we can take it still further. "Point Five" would go into that "10" twenty times. "Point One" would go into that "10" a hundred times.
Please note that the smaller the number, the more of it will go into that "10" - or any other number over zero! One can also say that the closer you get to zero, the more of that increasingly small quantity will go into that "10" - or any other number over zero.
Thus when you get down to a "zeroth" particle, that could go in to "10" (or any other number over zero) an infinite amount of times.
What does it mean to say that mass and weight are proportional to each other?
It means that if one increases, so will the other. More precisely, if one increases by a certain factor, the other will increase by the same factor.The relationship is as follows:
weight = mass x gravity
Basically, if the gravitational attraction doesn't changes, for example you are observing two different masses close to Earth's surface, then gravity (which close to Earth's surface is about 9.8 newton/kilogram) can be said to be the "proportionality factor".
In general, if a number "b" is proportional to another number "a", that means that there is a constant "k" such that:
b = ka
("b" is equal to "a", multiplied by the proportionality factor).
How do you work out the index number?
Index numbers are usually expressed by setting some selected value as 100 and converting all other numbers to an index relative to that base.
So, for a simple index, if the value y(0) is set to 100, then the index for the value y(k) is y(k)/y(0)*100.
The calculations become more complicated if the index is for a collection of items. In such cases, a number of different "sub-indices" need to be combined together. The combined index is calculated as a weighted average of the component sub-indices, with the weights based on the importance of each su-index in the base period (base-weighted) or in the current period (current-weighted).
Is 5 pounds of sugar bigger than 75 oz of chocolate?
5 x 16 = 80 oz sugar
so 5lb has more mass than 75 oz
