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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
When or is a qualifier in Venn diagrams what does it mean?
An element in the set A or B is one that is in the union of the two sets. It can be in A or B or both.
What was the cost of food in Australia in the 1960s?
The Australian Bureau of Statistics measures changes over time in the price of a theoretical ‘basket’ of goods and services which account for a high proportion of expenditure by metropolitan households. This ‘basket’ covers a wide range of goods and services arranged in eleven groups, including food. These data are collated into 'The Consumer Price Index' (CPI) released every three months.
In the period 1960-1969 the average CPI was 15.1
In the latest period for which data are available (as at the time of writing, March quarter 2007) the CPI was 155.6
So the 'cost of living' as measured by the Australian CPI has increased by about 930% from the 1960s to now. This means that $100 in today's currency had the same purchasing power as about $10.75 in the 1960s.
That is, the cost of goods and services (including food) in Australia in the 1960s was, roughly speaking, 1/10th what it is now. But bear in mind that's in relation to everything else such as wages and economic conditions at that time.
How would you define symmetry?
Identical construction across a boundary, e.g. a line.
There is also rotational symmetry.
the value of
Does Godels Incompleteness Theorem imply axioms do not exist?
No, not at all. The Incompleteness Theorem is more like, that there will always be things that can't be proven.
Further, it is impossible to find a complete and consistent set of axioms, meaning you can find an incomplete set of axioms, or an inconsistent set of axioms, but not both a complete and consistent set.
The parabola shape is magnified. If you keep the same scale for the graph, the parabola will look wider, more flattened out.
11 NCERT maths text book solved answers?
On Topperlearning you can fins class 11 NCERT Maths textbook Solved answers.
topperlearning.com/learn/text-book-solutions/ncert/cbse/class-11/b101c3e9
Under what condition the distance and displacement are equal?
The magnitude of displacement is equal to distance traveled when motion is in a straight line.
Establishing equivalence depends on the definition of parallel lines. If they are defined as lines which cannot ever meet (have no point in common), then the relation is not reflexive and so cannot be an equivalence relation.
However, if the lines are in a coordinate plane and parallel lines are defined as those which have the same gradient then:
- the gradient of a is the gradient of a so the relationship is reflexive ie a ~ a.
- if the gradient of a is m then b is parallel to a if gradient of b = m and, if the gradient of b is m then b is parallel to a. Thus the relation ship is symmetric ie a ~ b <=> b ~ a.
- If the gradient of a is m then b is parallel to a if and only if gradient of b = gradient of a, which is m. Also c is parallel to b if and only if gradient of c = gradient of b which is m. Therefore c is parallel to a. Thus the relation is transitive, that is a ~ b and b ~ c => a ~ c.
The relation is reflexive, symmetric and transitive and therefore it is an equivalence relationship.
Formula for Radius of Cylinder , closed on both ends, given its Surface Area and Height: Where : R = Radius, π = 3.1428, S = Surface Area of the Cylinder and H = Height of the Cylinder We start with formulas for the circle (Area = πR2 ) , then factor in the height (or altitude) H that forms the cylinder. Step 1: Starting Surface Area Formula: S = (2πR2 + 2πRH) Step 2: Then, rearranging the above, we get : (R+H/2) 2 = (S / 2π + H2 /4)Step 3: And , finally: R = - H /2 + √ (S / 2π + H2 /4) Example: If : S = 98, H = 14 ..Then R = 1.037
What is Godel's incompleteness theory?
Gödel's incompleteness theorem was a theorem that Kurt Gödel proved about Principia Mathematica, a system for expressing and proving statements of number theory with formal logic. Gödel proved that Principia Mathematica, and any other possible system of that kind, must be either incomplete or inconsistent: that is, either there exist true statements of number theory that cannot be proved using the system, or it is possible to prove contradictory statements in the system.
Which polygons do not tessellate?
Pentagons, decagons, and octagons will not tessellate. In order to create a tessellation, the sum of the angles at a point must be 360.
What five digit number is greater than 20000 but less than 30000?
There are 9999 possibilities; they are the numbers from 20001 to 29999 inclusive.
How can you prove there is no largest prime number?
No. No matter how large of an example you choose, someone always can find a larger number (of any kind), because the upper range of number is infinite.
If you take all the known prime numbers and multiply them together, then add 1 to the result, you will have a number that is not divisible by any of the known prime numbers. This number will either be prime or have prime factors that were not previously known. So, in this way, you can always find a new prime number or a number that is a multiple of new prime numbers. If the known prime numbers include all the prime numbers up to the largest known, the new ones must be larger.
Why is the Derivative of 'e raised to x' equal to 'e raised to x'?
the number e is by definition the number which raised to x will produce a graph such that at every point on the graph the slope of the graph is equal to x.
In otherwords, the answer to your question is because that is the way e is defined.
IDK... I saw e^x defined as a power series.
Consider: Let y = e^x
Since x is real (by assumption) then
ln(y) = x, where ln(t) is the natural logarithm of t. Now differentiate with respect to x
1/y * (dy/dx) = 1 Multiplying both sides by y, we get
dy/dx = y = e^x. This fits with the first definition but is more rigorous.
How do you get a percentage from a number?
Multiply it by 100 and add a percentage sign.
For example,
2.5 = 250%
-0.376 = -37.6%
What was Fermat's original proof of his last theorem?
Fermat's last theorem says there does not exist three positive integers a, b, and c which can satisfy the equation an + bn = cn for any integer value of n greater than 2. (2 with be pythagoran triples so we don't include that) Fermat proved the case for n=4, but did not leave a general proof. The proof of this theorem came in 1995. Taylor and Wiles proved it but the math they used was not even known when Fermat was alive so he could not have done a similar proof.
Does a parallelogram have diagonals bisect each other?
Yes every parallelogram has bisecting diagonals
How do you prove that order of a group G is finite only if G is finite and vice versa?
(1). G is is finite implies o(G) is finite.
Let G be a finite group of order n and let e be the identity element in G. Then the elements of G may be written as e, g1, g2, ... gn-1. We prove that the order of each element is finite, thereby proving that G is finite implies that each element in G has finite order. Let gkbe an element in G which does not have a finite order. Since (gk)r is in G for each value of r = 0, 1, 2, ... then we conclude that we may find p, q positive integers such that (gk)p = (gk)q . Without loss of generality we may assume that p> q. Hence
(gk)p-q = e. Thus p - q is the order of gk in G and is finite.
(2). o(G) is finite implies G is finite.
This follows from the definition of order of a group, that is, the order of a group is the number of members which the underlying set contains. In defining the order we are hence assuming that G is finite. Otherwise we cannot speak about quantity.
Hope that this helps.
What is the sum of degrees of all vertices in an undirected graph is twice the number of edges?
It is a true statement.
Given an arbitrary odd natural number greater than five, x, let y = x - 3, then y is an even number greater than 2. By assumption we have that y is the sum of two primes, say y1 and y2, but then x = y1 + y2 + 3 (which is the sum of three primes).
What are some geometry terms that begin with the letter a?
go to http://library.thinkquest.org/2647/geometry/glossary.htm#b and find out for yourself one off the top of my head is angle
How was it determined that the tangent of pi divided by 4 is 1?
As tan(x)=sin(x)/cos(x)
and sin(pi/4) = cos(pi/4) (= sqrt(2)/2)
then tan(pi/4) = 1
