How to prove that e is irrational? How to prove that e is an irrational number?

How to prove the existence of irrational numbers

Truth Any rational number is either a single integer or a fraction (finite decimal or infinite cyclic decimal). An integer and a fraction are both expressed in terms of the ratio of two integers, which is the property of a rational number. An isosceles with a right-angled edge of 1 and a diagonal edge of X. According to the Pythagorean theorem, the square of X =1...

Truth Any rational number is either a single integer or a fraction (finite decimal or infinite cyclic decimal). And integers and fractions can be expressed in terms of the ratio of two integers, which is the property of a rational number. An isosceles triangle with a right-angled edge of 1 and a diagonal edge of X. According to Pythagorean theorem, the square of X =1...

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1. How to prove that root 2 is irrational
2. 2 To the 2005 power minus 2 to the 2004 power minus 2 to the 2003 power minus ""minus 2 to the 2th power minus 2 to the 2th power minus 1 equals?
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5. Definition of irrational numbers
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11. Is there any difference between transcendental number and irrational number? Is π a transcendental number also an irrational number?
12. The irrational numbers with two sums of 1 are:(5 pairs)
13. Write two irrational numbers greater than -6 and less than -5
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15. The following statements are correct:() A. There is no minimum real number B. Rational numbers are finite decimals C. Infinite decimals are irrational numbers D. With roots The following statements are true () A. There is no minimum real number B. The rational number is a finite decimal C. Infinite decimals are irrational D. Numbers with roots are irrational The opposite of (3-√3) is The following statements are correct:() A. There is no minimum real number B. Rational numbers are finite decimals C. Infinite decimals are irrational numbers D. With roots The following statements are true () A. There is no minimum real number B. Rational is a finite decimal C. Infinite decimals are irrational D. Numbers with roots are irrational The opposite of (3-√3) is
16. We know that root 3 is an irrational number, it is an infinite non-recurring decimal, and 1< root 3<2, we call 1 the integer part of root 3, (Link above) Root 3-1 as decimal part of root 3. Using the above knowledge, can you determine the integer and decimal parts of the following irrational numbers? (1) Root number 10;(2) root number 88
17. Three times the root number 49 I through the calculator calculation found that it is a finite non-recurring decimal, not irrational number ah! Record the number that the calculator has calculated the root number 49 three times, bring it back in for calculation. Multiply it by the third power and it equals 9. Then isn't the root number 49 three times a rational number? Three times the root number 49 I found by calculator calculation it is a finite non-recurring decimal, not irrational number ah! Record the number that the calculator calculates the root number 49 three times and bring it back in for calculation. Multiply it by the third power and it equals 9. Then isn't the root number 49 three times a rational number?
18. You know that root 2 is an irrational number, and irrational numbers are infinite non-recurring decimals, so we can not write all the decimals of root 2, so small The root 2-1 is used to represent the decimal part of the root 2. Do you agree with Xiao Ming's representation? In fact, Xiao Ming's representation is reasonable, because the integer part of root 2 is 1. Subtract this number from its integer part, and the difference is the decimal part. Ask: Given 10+ root 3=x+y, where x is an integer and 0< y <1, find the opposite number of x-y.
19. How to judge whether the square root of a number is irrational or rational 123
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