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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.
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.
Will additive inverse always equal 0?
When a number is added to its additive inverse, the result is always 0.
