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Axioms cannot be proved.

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โˆ™ 2015-07-12 14:25:21
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Q: Axioms must be proved using data?
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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 elements is or are necessary for a geometric proof?

A statement to prove. It may be a theorem or not.A starting point that is based on information that is given.A sequence of steps based on logical application of axioms or theorems (in geometry or mathematics).These must conclude with the statement that you set out to prove.An alternative (reductio ad absurdum) is to start with the assumption of the truth of the negation of the statement that you wish to prove. Again using logical methods, show that this must lead to a contradiction and therefore, the assumption must be false and thus the statement must be true.


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.


Can interquartile range be used for any data eg data below the lower quartile to find if the data is spread out or close together or must we use the lower quartile for data below the lower quartile?

No, interquartile range cannot be for any data. The lower quartile for data must be used below the lower quartile.


Do you form a hypothesis before collecting data?

Yes. The data must not be allowed to influence the choice of the hypothesis.

Related questions

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 a hypothesis to become a theory?

A hypothesis become a theory if it is proved by experimental data. tested; conclusion (apex)


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 must be done BEFORE using the Subtotal command to add subtotals to your data?

Sort the Data


Civil cases must be proved by?

A civil case must be proved by a preponderance of the evidence.


What does it mean for a hypothesis to be testable?

The hypothesis must be able to be proved true or false.


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.


Which type of statement must be proven true in geometry?

Every statement apart from the axioms or postulates.


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.


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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 information must be included in a material safety data sheet?

Material safety data sheets must include what the hazards are for using this specific material. They must also have the do's and don't's of the material in which the sheet has information about.

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