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What else can I help you with?
What statement applies to theorems?
Must Be Proved Before They Can Be Accepted As True
Can a counterexample prove that the angles of a triangle need not add up to 180 degrees?
Yes - if such a counterexample can be found. However, using only the Euclidean axioms and logical arguments, it can be proven that the angles of a triangle in a Euclidean plane must add to 180 degrees. Consequently, a counterexample within this geometry cannot exist.
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.
Does a postulate need to be proved?
yes no. ( a second opinion) A postulate is assumed without proof. Postulate is a word used mostly in geometry. At one time, I think people believed that postulates were self-evident . In other systems, statements that are assumed without proof are called axioms. Although postulates are assumed when you make mathematical proofs, if you doing applied math. That is, you are trying to prove theorems about real-world systems, then you have to have strong evidence that your postulates are true in the system to which you plan to apply your theorems. You could then say that your postulates must be "proved" but this is a different sense of the word than is used in mathematical proving.
How do you know that various mathematical statements are true?
You start with a set of definitions and "self evident" axioms. These cannot be proven or disproved. Using the rules of mathematical logic you then deduce other statements theorems). If the axioms are true, then these theorems must also be true. You can then use the axioms and the theorems to derive more true statements and so on. Once proven, you can assume that they are true without having to go back to the axioms every time. Euclid formalised geometry in this fashion and all was well until his parallel postulate (an axiom) was questioned. The original was phrased differently (and in Egyptian, I guess), but it can be paraphrased as follows: "Given a straight line and a point outside the line, there is exactly one line that goes through the point and is parallel to the original line." Mathematicians in the 19th century found that they could develop axiomatic geometries replacing this postulate with its two alternatives: no parallel lines or many parallel lines, along with the other Euclidean axioms. They found that these geometries were wholly consistent. So, you could have a perfectly good axiomatic geometry with Euclid's parallel postulate as well as with its negations! Bertrand Russell tried to do the same for mathematics but failed. Then, in 1931 Kurt Godel showed that Russell's project was doomed from the start. Godel's incompleteness theorem proved that any (non-trivial) axiomatic system that was capable of arithmetic had to have statements which could be true and false - both versions were valid within the system. However, you would need to be working with mathematics at a very high level before you need to deal with the issue of incomleteness.
Who proved that it is impossible to give an explict system of axioms for all the properties of whole numbers?
In simple terms, Kurt Godel, showed that any axiomatic system must be incomplete. That is to say, it is possible to make a statement such that neither the statement nor its opposite can be proved using the axioms. I expect this is the correct answer though I believe that he proved it for ANY axiomatic system in mathematics - not specifically for whole numbers.
What must happen for to a hypothesis to become a theory?
A hypothesis become a theory if it is proved by experimental data. tested; conclusion (apex)
What does it mean for a hypothesis to be testable?
The hypothesis must be able to be proved true or false.
Civil cases must be proved by?
A civil case must be proved by a preponderance of the evidence.
Which type of statement must be proven true in geometry?
Every statement apart from the axioms or postulates.
What axioms must be satisfied for a collection of subsets to be called a topology on a set?
There are three axioms that must be satisfied for a collection of subsets, t, of set B to be called a topology on B.1) Both B and the empty set, Ø, must be members of t.2) The intersection of any two members of t must also be a member of t.3) The union of any family of members of t must also be a member of t.If these axioms are met, the members of t are known as t-open or simply open, subsets of B.See related links.
What is a data capture form?
Before setting up a database the data must be collected. This can be done using a data capture form.
Methods for data processing?
Data in datawarehouse must be processed before using it. There are three steps in data processing extraction, transformation and loading.
When using data from population genetics research the sample must be?
The sample must have a high probability of representing the population.
How secure is my data if I use a wireless service?
The data is well secured when using wireless service. But before transferring the data it must be encrypted for its security. Sometimes there may be data packet loss.
When collecting data during an experiment what must a scientist avoid using that will interfere with the hypothesis?
Emotions.
Why do you do proofs in geometry?
You start out with things that you know and use them to make logical arguments about what you want to prove. The things you know may be axioms, or may be things you already proved and can use. The practice of doing Geometry proofs inspires logical thinking, organization, and reasoning based on facts. Each statement must be supported with a valid reason, which could be a given fact, definitions, postulates, or theorems.
