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Is inductive or deductive reasoning the best way to approach a geometric proof?
Please remember proof gives absolute truth, which means it HAS to be true for all cases satisfying the condition. Hence, inductive reasoning will NEVER be able to be used for that ---- it only supposes that the OBSERVED is true than the rest must, that's garbage, if it's observed of course it's true (in Math), no one knows what will come next. But it's a good place to start, inductive reasoning gives a person incentive to do a full proof. Do NOT confuse inductive reasoning with inductive proof. Inductive reasoning: If a1 is true, a2 is true, and a3 is true, than a4 should be true. Inductive Proof: If a1 is true (1), and for every an, a(n+1) is true as well (2), then, since a1 is true (1), then a2 is true (2), then a3 is true (2). You see, in inductive proof, there is a process of deductive reasoning ---- proving (1) and (2). (1) is usually, just plugin case 1. (2) provides only a generic condition, asking you to derive the result (a (n+1) being true), that is deductive reasoning. In other words, proof uses implications a cause b, and b cause c hence a cause c. Inductive says though a causes c because I saw one example of it.
What is the difference between reasoning and inference?
Reasoning is different from inference because reasoning is a matter of using very little fact to make an accurate deduction towards a certain end. Inferences only come as a result of a test done to guide a certain view point.
What features of an argument make it inductive reasoning?
One AnswerInductive reasoning is a form of logical reasoning that begins with a particular argument and arrives at a universal logical conclusion. An example is when you first observe falling objects, and as a result, formulate a general operational law of gravity.A critical factor for identifying an argument based on inductive reasoning is the nature relationships among the premises underlying the propositions in an argument. Logical reasoning exists in an argument only when a premise or premises flow with logical necessity into the resulting conclusion. Hence, there is no sequence.The following is an example of an Inductive Argument:Premise 1. You know that a woman named Daffodil lives somewhere your building.Premise 2: Daffodil has a shrill voice.Premise 3. You hear a woman in the apartment next door yelling with a yelling with a shrill voice.Conclusion: It is likely that the woman fighting in the apartment is Daffodil.Note how the detailed premises logically flow together into the conclusion. This is the hallmark of inductive reasoning.Another AnswerI have heard of a mathematical proof that quantifies inductive reasoning through patterns in numbers, its called Occums Razor.Another AnswerThe information contained in the premises of an argument is supposed to provide evidence for its conclusion. In a good (valid) argument, they do; the conclusion follows logically from the premises. In a bad (invalid) argument, they do not.When the evidence provided by the premises is conclusive, or, minimally, supposed to be conclusive, the argument is a deductive one; otherwise, it is inductive.To use the metaphor of containment, in a valid deductive argument the information contained in its conclusion is always equal to or less than the information provided by its premises. For example, where 'p' stands for any proposition, the argument: "p, hence p" is valid (even though it's trivial). The information in the conclusion is obviously the same as the information in the premise. (In an actual case, this valid argument would be "sound" if the premise were true, and it would be valid but "unsound" if the premise were false.)By way of contrast, in an inductive argument, the information in the premises is always weaker than the information in the conclusion.For example, suppose that all the senators from a certain state have been male. Someone might argue that, since the first senator was male and since the second senator was male and since the third senator was male and so on, then the next senator will also be male. In this case, the information contained in the conclusion is not already contained in its premises (because its premises say nothing about the next senator). Is this, then, a successful argument?Obviously, it is not in the sense that there is a logical gap between the information contained in the premises and the information contained in the conclusion. On the other hand, some might argue that the premises provide some, but not conclusive, evidence of the truth of the conclusion. It might, in other words, be more likely that the next senator would be male, but that is not for certain.Therefore, in a deductive argument, the relevant evidence is, if true and the argument is valid, conclusive.However, in an inductive argument, the evidence provided by all the premises is never conclusive.CautionPeople often confuse inductive and deductive arguments. inductive arguments often reason from a set of particulars to a generality; deductive arguments often reason from a generality to a set of particulars. For example, if I see three robins (the bird, not Batman's sidekick) and they all have red breasts, then I can use inductive reasoning to say that all robins have red breasts (I start with what I've seen and make a general rule about it). Once I've made the rule that all robins have red breasts, then I can use deductive reasoning to say that the next robin I see will have a red breast (I start with a general rule and make a statement about a particular thing I will see).However, there are deductive arguments that move from general premises to general conclusions. Eg., All dogs are canines. All canines are mammals. Therefore, all dogs are mammals. And inductive arguments that move from particulars to particulars. Eg., These shoes are like the ones I bought last year at Zmart. The ones I bought last year are still wearable so these shoes are likely to be wearable too.
When you subtract a positive integer from a negative integer the result is always positive?
Yes because you are always adding.
What is true about two odd numbers?
When you add them, you always get an even number; when you multiply them, the result is always odd.
Inductive reasoning is empirical in nature which means that it is based on?
Inductive reasoning use theories and assumptions to validate observations. It involves reasoning from a specific case or cases to derive a general rule. The result of inductive reasoning are not always certain because it uses conclusion from observations to make generalizations. Inductive reasoning is helpful for extrapolation, prediction, and part to whole arguments.
What is a conclusion reached through inductive reasoning?
Deductive reasoning goes from a general to a specific instance. For example, if we say all primes other than two are odd, deductive reasoning would let us say that 210000212343848212 is not prime. Here is a more "classic"example of deductive reasoning. All apples are fruits All fruits grow on trees Therefore, all apples grow on trees
Is inductive or deductive reasoning the best way to approach a geometric proof?
Please remember proof gives absolute truth, which means it HAS to be true for all cases satisfying the condition. Hence, inductive reasoning will NEVER be able to be used for that ---- it only supposes that the OBSERVED is true than the rest must, that's garbage, if it's observed of course it's true (in Math), no one knows what will come next. But it's a good place to start, inductive reasoning gives a person incentive to do a full proof. Do NOT confuse inductive reasoning with inductive proof. Inductive reasoning: If a1 is true, a2 is true, and a3 is true, than a4 should be true. Inductive Proof: If a1 is true (1), and for every an, a(n+1) is true as well (2), then, since a1 is true (1), then a2 is true (2), then a3 is true (2). You see, in inductive proof, there is a process of deductive reasoning ---- proving (1) and (2). (1) is usually, just plugin case 1. (2) provides only a generic condition, asking you to derive the result (a (n+1) being true), that is deductive reasoning. In other words, proof uses implications a cause b, and b cause c hence a cause c. Inductive says though a causes c because I saw one example of it.
What is a logical conclusion?
A logical conclusion is a judgment or result reached through reasoning and evidence that follows logically from the premises or information presented. It is the final step in the process of deductive or inductive reasoning where one can infer what is most likely or probable based on the information available.
Is deductive reasoning more important than inductive reasoning?
Both are equally important. Inductive reasoning is when one makes a conclusion based on patterns; deductive reasoning is based on a hypothesis already believed to be true. However, deductive reasoning does give a more "solid" conclusion because as long as the hypothesis is true, the conclusion will most likely to be true. An example is saying that all dogs are big; Harry is a dog, so it must be big. Since the hypothesis all dogs are big is false, Harry may not necessarily be big. If I change my hypothesis to be all dogs are mammals, thus concluding that Harry is a mammal since it is a dog, I would be correct, for I changed my hypothesis to a true fact. Using inductive reasoning, on the other hand, may result in a false conclusion. For example, since I am a human and I have brown hair, one could use inductive reasoning to say all humans have brown hair, which would be false. So, to sum it up, both inductive and deductive reasoning are important, but deductive reasoning is usually more reliable since as long as the hypothesis one's conclusion is based on is true, the conclusion itself will usually be true.
Is instinct the same as reasoning?
No, instinct is an action which is NOT the result of reasoning.
What does an appellate judge issue if he or she agrees with the appellate court's decision but not its reasoning?
The judge issues a concurring opinion if he or she agrees with the result but not with the reasoning behind the result.
A justice who voted with the majority might express the reasoning in a?
concurring judgment A concurring judgment is one in which the reasoning is different, but not the end result. (A dissenting judgment, however, is one that differs in the result from that of the majority.)
What are Strengths and weaknesses of deductive and inductive research approaches?
Inductive research approaches are more widely used than Deductive by the scientific community, but they both have there strength and weaknesses. Inductive method: -Strengths: The inductive method produces concrete conclusions about nature that are backed by a variety of observational evidence. When one of an inductive arguments premises are perceived as false, other observational evidence can be added to the premises to save the argument, this is not the case with deductive reasoning. -Weaknesses: The inductive method produces conclusions that go beyond what there premises warrant. In other words, inductive arguments take a limited amount of observations to provide a universal conclusion, which could still be false. For example, someone observes 10,000 dogs and finds that they all have flees, then inductively concludes that all dogs have flees. This is a situation where overwhelming observational evidence (10,000 dogs have flees) points to an inductively reasoned false conclusion (All dogs have flees). Deductive Method: -Strengths: Deductive reasoning dosent require painstakingly observing a variety of observational evidence to reach a conclusion. One can start off with a generally accepted axiom, or statement, and deduce conclusions based on that axiom. -Weaknesses: Deductive reasoning can make permanent the logical fallacies we have today. In other words, if you use an axiom to deduce a variety of conclusions, and that axiom turns out to be false, all of the conclusions following that axiom are false as a result. hope this helps!
Does surgery always result in arthritis?
No, surgery does not always result in arthritis.
How can you prove a conjecture false?
The word "conjecture" can be taken a number of ways. If the "conjecture" involves an inference based on false or defective information, you need only show convincing or conclusive evidence that the information is false or faulty. If the "conjecture" is the result of surmise or guessing, then it is nothing more than a guess itself, and, therefore, has no basis in fact or logic. If the "conjecture" is an unproven mathematical hypothesis, you will need to disprove its validity from its basis. Start with the basic crux of the problem and work step by step until you disprove (or prove) the hypothesis to be untrue (or true). Make sure you have good arguments and sound mathematics.
Which is not a result of scientific theory?
Personal beliefs or opinions are not a result of scientific theory. Scientific theories are based on empirical evidence and reasoning, not on subjective views or perspectives.
