## Proofs

Parent Category: Math and Arithmetic
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.
You can use a variety of postulates or theorems, among others:   SSS (Side-Side-Side)   ASA (Angle-Side-Angle - any two corresponding sides* and a  corresponding angle)   SAS (Side-Angle-Side - the angle MUST be between the two sides,  except:)   RHS (Right angle-Hypotenuse-Side - this...
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...
The obvious answer is 5,000,000 but... If the 1000000 is in base 2 (binary) and the five is in base 10 (decimal) then 1000000 equals 64 in base 10; 64x5 = 320 which is 101000000 in base 2.
You really can't "prove" the formula. You use it. You first squarethe base ' b '. Then, you multiply that number by the height' h' . Then, you divide the product of the base squared andheight by 3. Boom! You get your answer. In my school, we get aformula sheet with all the formulas we will need to...
can be written, where each Qi is a sum of squares of linear combinations of the Us. Further suppose thatwhere ri is the rank of Qi. Cochran's theorem states that the Qi are independent, and each Qi has a chi-squared distribution with ri degrees of freedom.[citation needed]Here the rank of Qi should...
a ≠ 0, LCD = a33/a + 2/a2 - 1/a3= (3/a)(a2/a2) + (2/a2)(a/a) - 1/a3= 3a2/a3 + 2a/a3 - 1/a3= (3a2 + 2a -1)/a3
theorem always needs proof
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...
  == Answer ==   Lagrange theorem states that the order of any subgroup of a group G must divide order of the group G. If order p of the group G is prime the only divisors are 1 and p, therefore the only subgroups of G are {e} and G itself. Take any a not equal e. Then the set of all integer...
  In chemistry, 46 is the atomic number of Palladium.    In human biology, there are 46 human chromosomes. There are  22 pairs of autosomes and one pair of sex chromosomes.   In geometry, the name of a 46 sided shape is called a  tetracontakaihexagon.  
if divides both and , then it will also divide therefore will divide thus The last part comes from the fact that: if gcd(x,y)=g, then . As proof: Since g|x and g|y, let x=kg, and y=jg, then we have so g|(mx+ny).
7 Marsi Festën e mësuesit Ne do ta festojmë Lulet më të bukura Ne do ti dhurojmë. Vijmë tek ti mësues Buzëqeshjen ta dhurojmë Kënga krahët reh si flutur Midis jush jam e lumtur.
Yes one and one third times one and one half
If the signal is bandwidth to the fm Hz means signal which has no frequency higher than fm can be recovered completely from set of sample taken at the rate
Putting a question mark at the end of a few words does not make it  a sensible question. Please try again.
According to Wikipedia, "This was proved in 1768 by Johann Heinrich Lambert."
The answer will depend on the two triangles in question. Since that information is not provided it is not possible to give a sensible answer.
The value of pi has never been proven becauase it is an irrational number which can not be expressed as a fraction
243112609-1. It has almost 13 million digits.
All opposite sides of a die are meant to add up to 7.   So:   1 and 6   2 and 5   3 and 4    This is also part of why the most common dice rolls (involving two  dice, in a game of monopoly for example) is 7 -- because every  number can match with another number to give a sum of 7.
The essence of the proof is simply to complete the square for a generalised quadratic equation. Like this: ax 2 + bx + c = 0 Take 'a' outside: a[x 2 + bx/a + c/a] = 0 Divide through by 'a': x 2 + bx/a + c/a = 0 Complete the square: (x + b/2a) 2 - b 2 /4a 2 + c/a = 0 Rearrange to find x: (x + b...
A theorem is a proved rule but an axiom cannot be proven but is stated to be true.
Any negative integer can be factored to -1 times its positive value. Because negative one times itself is positive one, when multiplied by each other they cancel out. So if you're multiplying a negative integer A by a negative integer B. Replace A and B with -1*|A| and -1*|B| (You can do this...
  The acronym "HUCA" refers to the "House Un-American Activities Committee" (also known as the House Committee on Un-American Activities), a committe of the U.S. House of Representatives.   For Wikipedia's article on this subject, see:   http://en.wikipedia.org/wiki/House_Un-American...
More information is needed. Your coin is almost certainly British, but you also need to supply its denomination and condition. Please post a new question so that it will be possible to ID your coin. The motto is several words, not one, and variations of it are found on all British coins. It's...
If we assume that the sqare root of 5 is a rational number, then we can write it as a/b in its simplest form, where a and b have no common factors. Therefore 5 = a2/b2Therefore 5b2 = a2Therefore a2 is divisible by 5, because b2 is an integerTherefore a is divisible by 5, because 5 is a prime number....
convention, most people would be more comfortable with cm or mm so feel free to use them
The negation of a statement is the opposite proposition to the original statement. Specifically, exactly one of the negation and the original proposition must be true, not both or neither. In mathematical analysis, "for all" quantifiers must be replaced with "existential" quantifiers and visa versa,...
Assuming you work with two variables (like x and y) only: if the graph is a vertical line, e.g. x = 5, then it is not a function. Otherwise it is.
== Answer ==   I don't know why there should be 4 laws (=axioms) specifically. In mathematics you can choose whatever system of axioms and laws and work your way with those. Even "logic" (propositional calculus) can be redefined in meaningful ways. the most commonly used system is Zermolo...
In mathematical terms it is simple. In physical terms it is very difficult - for two related reasons. Having said that, there have been successful attempts. In late 2011 students from St. Mark's School in Southborough, Massachusetts succeeded in folding a paper in half 13 times. They used toilet...
== Proving the Identity ==   When proving an identity, you may manipulate only one side of the equation throughout. You may not use normal algebraic techniques to manipulte both sides.   Let's begin with the identity you wish to prove.   cos2x - sin2x ?=? 2cos2x - 1   We know that sin2x ...
50\$ at a flea market,100\$ at a antique show,200\$ at a antique shop,
208 times, from 1 to 100 there r 11 nine such as 9 , 19 , 29, 39, 49,59, 69,79, 89, 99 its prove there are 11 nines so up to 800 there are 11*8=88 nines and from 900 to 1000 there are 100(901, 902,903......)+ 10 ( 990,991,992.....)+10 (909,919,929,939....)=120 that means there are in total 88+120...
== Answer ==   The easiest way is through easy websites such as this:   http://wiki.answers.com/Q/What_are_the_factors_of_math   Alternatively, you can use prime factorization. In this case, 1800 = 2*2*2*3*3*5*5. Thus any divisor contains at most three factors of 2; that means there are...
For this translation, you need to replace every occurence of "x" with "x-3", and every occurence of "y" with "y+5".
Study shows that pure water density is 1gm/cc. This might be at lower altitudes because that 1gm could not be 1gm anymore at high altitudes. Salt water density is slightly higher thus it was said that ships float better at sea meaning that sea water has more bouyant force than pure water. 8^DIt...
Srinivasa Ramanujan, who was said by GH Hardy to have talent "in the same league as legendary mathematicians such as Gauss, Euler, Cauchy, Newton and Archimedes", passed away at the age of 32 in Chetput, Madras, India.
In Formal Logic proofs, the contradiction is represented with an inverted T (or upside-down T) as follows: ┴   The contradiction symbol can be introduced at any time a logical contradiction is encounterd, for example, all of the the following contradictory logical statements (using different...
Pythagoras is supposed to come up..! and also my teacher said it could be the first theorem! but don't forget there is constructions also and I'm not completely sure about those Thermos's. I hope this helped..!
he commandand me to help him with the lab report
We need to put an end to that fallacious rumor.
Assume that f:S->T is invertible with inverse g:T->S, then by  definition of invertible mappings f*g=i(S) and g*f=i(T), which  defines f as the inverse of g. So g is invertible.
2222= 3 mod 7 5555 = 4 mod 7 2222^5555 + 5555^2222 = (3^5)^1111 + (4^2)^ 1111 as it is a^n + b^n and n is odd so it is divisible by (a+b) 3^5 + 4^ 2 = 259 hence by 7 as 7 is a factor of 259
You can convert this to base ten by re-writing 3096 as a summation of hex powers: 3*16^3 + 0*16^2 + 9*16^1 + 5*16^0 = 12437 in base 10
No, only natural numbers (positive integers) can be prime.
A cyclic group of order two looks like this. It has two elements e and x such that ex = xe = x and e2 = x2 = e. So it is clear how it relates to the identity. In a cyclic group of order 2, every element is its own inverse.
Let G be the cyclic group generated by x, say. Ten every elt of G is of the form x^a, for some a
0 is an even number as it is exactly divisible by 2.
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...
depends on what you have.... one way is to see that the the triangles share two same angles, and one side with equal length...
The troposphere is also called the turbulent sphere because it is  the sphere with the most change. It has moving air currents,  clouds, storms, jet streams, strong and other weather phenomena  that affect weather patterns.
A counter example occurs when somebody makes a claim that all members of some category of things have a particular property, and then someone else proves that the claim is not true by showing an example of a thing in the category that does not have the property claimed. For example, if someone...
There are 47621/100 = 476.21 of them.
why doesn't wiki allow punctuation???   Now prove that if the definite integral of f(x) dx is continuous on the interval [a,b] then it is integrable over [a,b].   Another answer:   I suspect that the question should be:   Prove that if f(x) is continuous on the interval [a,b] then the...
Such statements are called postulates in geometry and axioms in other areas. Definitions are also accepted without proof, but technically they are abbreviations rather than statements.
Axioms and logic (and previously proved theorems).
Yes. This, of course, is under only the assumption that the two relations of element and containment are well defined relations between any two objects that are presumed to exist. Such a question can not be postulated if the empty set is absent from existence, so it follows the existence of the...
There are no irrational numbers in the value -5.72. All of the components of the value are represented by rational numbers. An irrational number is any number that cannot be represented by a fraction a/b where a and b are integers.-5.72 itself is rational as it can be represented by -572 / 100.The...
Its perimeter is half of its circumference plus its diameter
You cannot prove that because it's false
The eight (8) grouping symbols related to set theory include the following: ∈ "is an element (member) of"∉ "is not an element (member) of"⊂ "is a proper subset of"⊆ "is a subset of"⊄ "is not a subset of"∅ the empty set; a set with no elements∩ intersection∪ union
square no. Means reapeating the particular no. Twice. For ex. 1*  1equal 1, 4 * 4 equal 16, 7 * 7 equal 49. The no.s 1, 4, 49 are sq.  Nos . 2 * 3 equals 6 and 5 * 2 equalls 10 are not a square no. Two  identical no are multiplied and tie resultent is called a square  no. Any two identical nos...
Yes it is possible. If limit(f) > 0 then limit(loga(f)) = loga(limit(f)). All logarithmic functions loga(x) are continuous as long as x > 0. Where-ever a function is continuous, you can make that kind of swap.
The inverse of a rotation matrix represents a rotation in the opposite direction, by the same angle, about the same axis. Since M-1M = I, M-1(Mv) = v. Thus, any matrix inverse will "undo" the transformation of the original matrix.
The Mean Value Theorem states that the function must be continuous  and differentiable over the whole x-interval and there must be a  point in the derivative where you plug in a number and get 0  out.(f'(c)=0). If a function is constant then the derivative of  that function is 0 => any number...
The digit 9 in the number 89123 represents nine thousands.
Yes. A graph is bipartite if it contains no odd cycles. Since a tree contains no cycles at all, it is bipartite.
Given our hypothesis: An even number multiplied by an even number will always result in another even number.We can demonstrate that this is true by selecting any two even numbers and multiplying them together:8 x 10 = 80Clearly, our demonstration shows that our hypothesis is correct for...
to calculate velocity of fecal in castrated monkeys.
Error = Observed value - True Value.