If L1=1 and L2=2, we would just get the Fibonacci sequence. Recall that the Fibonacci sequence is recursive and given by: f(0)=1, f(1)=1, and f(n)=f(n-1)+f(n-2) for integer n>1. Thus, we have f(2)=f(0)+f(1)=1+1=2. If L1=1 and L2=2 then we would have L1=f(1) and L2=f(2). Since the Lucas numbers are generated recursively just like the Fibonacci numbers, i.e. Ln=Ln-1+Ln-2 for n>2, we would have L3=L1+L2=f(1)+f(2)=f(3), L4=f(4), etc. You can use complete induction to show this for all n:
As we have already said, if L1=1 and L2=2, then we have L1=f(1) and L2=f(2). We now proceed to induction. Suppose for some m greater than or equal to 2 we have Ln=f(n) for n less than or equal to m. Then for m+1 we have, by definition, Lm+1=Lm+Lm-1. By the induction hypothesis, Lm+Lm-1=f(m)+f(m-1), but this is just f(m+1) by the definition of Fibonnaci numbers, i.e. Lm+1=f(m+1). So it follows that Ln=f(n) for all n if we let L1=1 and L2=2.
Because both are based on strict rules of logical reasoning.
Argument
Deductive reasoning is a logical process in which a conclusion is drawn from a set of conclusions that contain no more information than is already available. This conclusion is logically true. . Inductive reasoning is a logical process in which a conclusion is proposed when it contains more information than the observations or experiences on which the conclusion is based. The terms of the conclusion is verifiable only in terms of future experience. For example, there is no certainty that a white crow will be found tomorrow, although past experience will make the occurance unlikely
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there r 4 logical operator not 3 AND, OR, XOR, and NOT
logical reasoning
Logical reasoning is a systematic method of arriving at a conclusion based on given information. It involves evaluating arguments, identifying patterns, and drawing valid inferences using a structured approach to problem-solving. It helps to think critically and make decisions based on evidence and sound reasoning.
Logical reasoning was a major concept in Enlightenment thinking.
Sound reasoning is correct, valid, logical, believable reasoning.
A logical person is someone who applies reasoning and critical thinking to make decisions and solve problems. They prioritize evidence, facts, and clear reasoning over emotions or biases. Logical individuals are able to see connections between ideas and make sound judgments based on sound reasoning.
a logical fallacy
providing relevant facts and statistics to support your argument, using logical reasoning to connect your points cohesively, and addressing potential counterarguments to strengthen your position.
ar·gu·ment, A course of reasoning aimed at demonstrating truth or falsehood: log·i·cal Reasoning or capable of reasoning in a clear and consistent manner. logical argument- a course of reasoning aimed at demonstrating a truth or falsehood; the methodical process of logical reasoning; Thesaurus.By it's definition, it's to separate truth from falsehood or fiction.
Logical reasoning is reasoning which follows the branch of philosophy known as logic. Logic elucidates the rules of correct reasoning.
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Reasoning
No. A mistake in reasoning is called a logical fallacy.