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No.
A conjecture itself has not been proved true (nor false), but is believed, on the evidence so far, to be true. If it is at some stage in the future actually proved to be false any proof based on it would immediately be useless as anything can be proved to be true from a false premise, and this includes false statements.
For example consider a father who always tells his child the truth and consider the statement a father gives his son: "If you are not in bed by 8pm then I will not read you a story".
If the child in not in bed by 8pm, then the father will not read them a story. ie if the premise of not being in bed by 8pm is true, it is proved that no story is read.
However, if the child is in bed by 8pm, the premise of not being in bed by 8pm is false (ie the child is in bed by 8pm) nothing can be inferred about a story being read: the father may read a story, or he may not read a story.
The conjecture concerns the time the child is in bed:
If the child is in bed by 8pm, and the father does read a story, the father made a true statement.
If the child is in bed by 8pm, and the father does not read a story, the father still made a true statement!
This may seem illogical (and cruel), but the father has only said what will happen if the child is not in bed by 8pm; he has said nothing about what will happen if the child is in bed by 8pm. It is very logical and is the "implies" (→) logic table:
T → T = T
T → F = F
F → T = T
F → F = T
If the first statement is true, the result is the truth of the second statement.
If the first statement is false, the result is true regardless of the truth of the second statement.
So if a conjecture is the first statement, only if it is [proved true] true does it say anything about the truth of the following statement.
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Explain the steps used to divide a polynomial by a polynomial?
You can find explanation and examples here: http://en.wikipedia.org/wiki/Polynomial_division
Do theorems need to be proved?
By definition, a theorem is a proven statement- until a proof is made for a statement, it is not a theorem but rather a conjecture. Whether you need to be able to reproduce the proof of a known theorem is another matter. If you trust the prover, I think you can make use of a theorem without knowing the proof. However, studying the proof can give you valuable insights into what the theorem really means and how it might be used. Also, reading proofs made by other people can help you prove you own theorems and write them up coherently.
Who believed that numbers could be used to explain the natural world?
Pythagoras believed numbers could be used to explain the natural world.
Which types of statements cannot be used to justify proof?
guess and conjeture
Can algebraic property be used to justify a statement in a geometric proof?
yes
What type of statement cannot be used to explain the steps of a proof?
A logically inconsistent statement.
Which of the following types of statement cannot be used to explain the steps of a proof Check all that apply?
Conjecture and Guess.
What types of statement can be used to explain the steps of a proof?
The corollaries types of statement is what is used to explain the steps of a proof.
What types of the statement can be used to explain the steps of a proof?
The corollaries types of statement is what is used to explain the steps of a proof.
Which of the following types of statement cannot be used to justify the steps of a proof check all that apply a guess b theorem c conjecture d postulate?
Guess Conjecture
Which types of statements can justify the steps of proof?
which of the following types of statement can be used to explain the steps of proof?
Can a theorem be used to explain the steps of a proof?
Yes- provided its proof does not depend on the result you are using it to prove.
Can the word conjecture be used as a verb?
Conjecture is a noun, the corresponding verb is to conject, meaning to form an opinion without proof.
What is used to support steps of a geometric proof?
Steps in a geometric proof do not require support
Can a postulate be used to justify the steps of a proof?
no
What do you use as reasons to support the steps of geometric proof?
the theorems and postulates used in the proof
What is never used to justify statements made in the proof of a new theorem?
a conjecture is never used , although postulates , previously proven theorems and definitions are used. so the answer is CONJECTURE. btw r u referring to the birmingham university chapter 2 speedback assignment?
