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Proofs
Proof means sufficient evidence to establish the truth of something. It is obtained from deductive reasoning, rather than from empirical arguments. Proof must show that a statement is true in all cases, without a single exception.
1,294 Questions
Three-fourth of a number is less than the fourth-fifth of the number by 3 find the number?
Let the number be x.
Then (4/5)x - (3/4)x = 3 iff (16/20)x - (15/20)x = 3 iff (1/20)x = 3 iff x=60.
So the number is 60.
Why is zero divided by zero undefined?
Zero divide by zero is zero. Any number divided by zero is zero........ :)
ex. ( 10/0= 0 )
A simple graph with n vertices and k components can have atmost how many edges?
In a connected component of a graph with Mi vertices, the maximum number of edges is
MiC2 or Mi(Mi-1)/2. So if we have k components and each component has Mi vertices
then the maximum number of edges for the graph is M1C2+M2C2+...+MKC2.
Of course the sum of Mi as i goes from 1 to k must be n since the sum of the vertices in each component is the sum of all the vertices in the graph which you gave as n.
Where MC2 means choose 2 from M and there are M(M-1)/2 ways to do that.
That would be...wait. Why don't you figure it out. There are 24 hours in a day. So take 24 from 36. You SHOULD get 12, which is half a day. So to answer your question, 36 is 1.5 days (1 and a half days)
How are linear equations and functions alike and how are they different?
A linear equation is a special type of function. The majority of functions are not linear.
What was stated in the gougu theorem?
The gougu theorem was the Chinese version of the Pythagorean theorem, they stated the same principle
Applications of vector calculus in real life?
That depends on what your "real life" consists of. If you sell merchandise at a supermarket, or do carpentry work, you won't need such advanced mathematics. If you work in the engineering fields, you might need it at some moment like with electromagnetic fields, gravitational fields and fluid flow. If you are an engineer you will come across vector calculus to handle three dimensional space.
What rule describes a translation that is 3 units to the right and 5 units down?
For this translation, you need to replace every occurence of "x" with "x-3", and every occurence of "y" with "y+5".
it is a shape with 4 parellel lines and it slanted on one side
How do you prove Schur's lemma?
CK(J) = {x Є K: jx = xj for all j Є J}.
Also, using the established theorem that "if J is a subset of ring K, then C(J) is a subring of K, and if an invertible element a of K belongs to C(J), then k-1 Є C(J)," we need only show that if g Є C* (C* being the set of non-zero elements of C), then g is an automorphism of E. Assuming non-triviality, g � 0, and there exists
b Є E such that g(b) � 0. For each h Є E there exists m Є K such that m(g(b)) = y since K is primitive. Thus: g(m(b)) = m(g(b)) = y, showing that g is surjective.
Finally to show g is also injective and thus an automorphism, we take a non-zero element w belonging to the kernel of g. For each z Є E some endomorphism would exist u Є K such that u(w) = z as K is primitive. Therefore:
g(z) = g(u(w)) = u(g(w)) = u(0) = 0, the zero endomorphism which is a contradiction. Hence g is injective and an automorphism of E.
Q.E.D.
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Hope this helps!!
Is an empty half plane still a convex set?
The answer depends on how it is halved. If the plane is divided in two by a step graph (a zig-zag line) then it will not be a convex set.
Prove the existence of triangles?
1. Given any line, there are at least two points on the line. Call them A and B.
2. Given any line, there exists at least one point in the plane that is not on the line. Call that point C.
3. Given any two points (A and C and, then B and C) there exists a straight line joining them.
The point C is not on AB so AB and AC are distinct. Similarly, AB and BC are distinct so that there are three lines that meet, in pairs, at three vertices - and that is a triangle.
What was the cost of foods in the 1960s?
The cost of a loaf of bread in the 1960's was 20 cents. The cost of a gallon of milk was 1.04 and bananas were 10 cents per pound.
What does three dots in a upside down triangle mean?
SYMBOLS USED IN WRITING
Three dots in a non-inverted triangle shape ( ∴ ) means 'therefore.'
Three dots in an upside-down triangle shape ( ∵ ) means 'because'.
SAFETY SYMBOLS
∵ is also used to mark a "threat".
For more information, see Related links below.
In general how many planes are there which contain any number of given points?
There are no planes containing any number of given points. Two points not the same define a line. Three points not in a line define a plane. For four or more points to lie in the same plane, three can be arbitrary but not on the same line, but the fourth (and so on) points must lie in that same plane.
What are two postulates that is not true about atom?
If they are known not to be true then they are no longer postulates but discarded theories.
What is a solution in which more solute can be dissolved?
A solution in which more solute can be dissolved has not reached saturation. It is an unsaturated solution.
Bayes theorm with one simple example?
First P(E|F) means the probability of E given F. Now, Bayes theorem gives us a way of calculating P(E|F) if we know P(F|E).
P(F|E) =(E|F)P(F) divided by
P(E|F)P(F) + P(E|F')P(F')
E = the event that an anabolic steroid detection test gives a positive result
F = the event that the athlete uses steroids
then
P(E|F) = probability that the test is positive for an athlete who uses steroids.
P(F|E) = probability that an athlete uses steroids given that the test is positive.
A drug test will detect steroid use meaning it show positive for an athlete who uses steroid 95% of the time. A rugby player has just tested poositive. The probability that he uses steroids is:
P(E|F) = 0.95 P(E|F') = 0.15 P(F) = 0.1 P(F') = 0.9P(E|F)=(0.95)(0.1) divided by
(0.95)(0.1) + (0.15)(0.9)
a) 1/16
b) 1/16
c) 1/256 [this answer was given, but it is unclear what part-c is even asking: The pattern occurs before what pattern? There are many variables which are unspecified and would affect the outcome.]
What is the most elegant proof in mathematics?
There are many beautiful proofs in Mathematics and one cannot say that any particular proof is the most elegant. But if I had to choose one, it would definitely be the proof that's associated with the Gödel's Incompleteness Theorem. It is Mathematics at its best. Read more about it from the related link given just below.
