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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 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
Find two numbers whose sum is 35 and whose difference is 9?
start with what you know: x + y = 35 x - y = 9 add them together: x + x + y - y = 35 + 9 resolve the rest of the facts: X + X = 44 X = 22 22 + y = 35 22 + y - 22 = 35 - 22 y = 13 confirm: 22 + 13 = 35 22 - 13 = 9
How many milliliters are in 1000 milligrams?
If you take 1000 milligrams of distilled water at 0 degrees centigrade, it will measure exactly 1 milliliter. Likewise, 1 kilogram of distilled water at 0 degrees centigrade is exactly 1 liter.
However, for other substances, the answer will differ. It depends on the volume of the substance that weighs 1000 mg.
For example, 1000 mg of lead (Pb) is far smaller in volume than 1000 mg of water (H2O), which is far smaller in volume of 1000 mg of gaseous Oxygen (O2).
ML is milliliters - a volume.
mg is milligrams - a weight.
1000 milliliters = 1 liter.
1000 milligrams = 1 gram.
How much is 1 year in seconds?
1 (normal) year is 31536000 seconds and a leap year is 31622400 seconds.
What side reads the same upside down or right side up?
Do you mean "Ambigram" ; a typographical design or art form that may be read as one or more words not only in its form as presented, but also from another viewpoint, direction, or orientation.
Why is it non set is asubset of all sets?
A "subset" means you can make it out of the pieces in the original set. No matter what set you begin with, you always have the option to choose no pieces at all--that creates the null subset.
