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从零补齐扎实的理论计算机数学基础！
介绍：
https://www.yuque.com/abser/mathincs/preview
例子：
https://www.yuque.com/abser/mathincs/theorem1.5.1

Theorem1.5.1. If 0 <= x <= 2,then -x^3+4x+1>0.

Question

Theorem1.5.1. If,then.

Solution

Proof. Assume . Then x, 2-x and 2+x are all nonnegative.

Therefore, the product of these terms is also nonnegative. Adding 1 to this product gives a positive number, so:

Multiplying out on the left side proves that

as claimed. 􏰐

Learn way

• You should practice this, learn how to write a Proof . You may do some scratchwork while you’re trying to figure out the logical steps of a proof. Your scratchwork can be as disorganized as you like—full of dead-ends, strange diagrams, obscene words, whatever. But keep your scratchwork separate from your final proof, which should be clear and concise.

• This is your first CLASS on math, show your search skill while you meet Strange Concept，also I would write some necessary Concept for you.

Homework

• Do you know about what nonnegative means?
• Please figure out why we know that the product of these terms is also nonnegative and how dare we use it without prove it.

also, you could write your answer as comment.

New Concept

Proof Method

method

In order to prove that IMPLIES :

1. Write,“Assume.”

2. Show that logically follows.

Logical Deductions

Logical deductions, or inference rules, are used to prove new propositions using previously proved ones.

A fundamental inference rule is modus ponens. This rule says that a proof of P together with a proof that P IMPLIES Q is a proof of Q.

Inference rules are sometimes written in a funny notation. For example, modus ponens is written:

Rule.

When the statements above the line, called the antecedents, are proved, then we can consider the statement below the line, called the conclusion or consequent, to also be proved.

A key requirement of an inference rule is that it must be sound: an assignment of truth values to the letters P, Q, ..., that makes all the antecedents true must also make the consequent true. So if we start off with true axioms and apply sound inference rules, everything we prove will also be true.

There are many other natural, sound inference rules, for example:

Rule.

Rule.

On the other hand,

Non-Rule.

is not sound: if P is assigned T and Q is assigned F, then the antecedent is true and the consequent is not.

As with axioms, we will not be too formal about the set of legal inference rules. Each step in a proof should be clear and “logical”; in particular, you should state what previously proved facts are used to derive each new conclusion.

3 replies

• 

  va1ner

  Yesterday 22:54

  1. A nonnegative integer is grater than or equal to 0
  2. The product of nonnegative integers can be seen as the sum of nonnegative integers,and when we refect the integers to objects in reality,obviously the sum wouldn't be negtive.

  ReplyDelete

• 

  飞云之下

  Today 09:32

  1.A nonnegative is a number bigger than 0.

  2.The product of nonnegative integers

  can be seem as the sum of nonnegative. so if we add a nonnegative to the non negative integers ,the sum of it is also

  no negative.

  ReplyDelete

• 

  Abser（杨鼎睿）

  Today 11:45

  @va1ner(vainer)@ 飞云之下(feiyunzhixia)

  By homework, I want you know

  the set is closed under addition, multiplication, and division.

  Think about why you did n’t think deeply here, and try to find these missing things which all have to learn.

  and there is wiki link :Positive_real_numbers