Find the answer or say "does not exist": (a) what is the smallest positive real number? (b) what is the smallest integer larger than 50? (c) what is the smallest rational number bigger than 1?

Q: (a) Prove that the real number p3 is an irrational number. That is, prove that If r is a positive…

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Q: Suppose that p is a prime integer greater than 1755. What is the largest possible value of (p,…

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Q: true or false? why. there exists a set of negative real numbers whose supremum is positive

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Q: -5a -7<12

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Q: • for any integers a, b, c, • n is not prime and p6 |n, where p; is the ith prime (i.e., p₁ = 2,p2 =…

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Q: Find the value of the following: 9!9!/10!6! If your answer is not an integer,  write it as an…

A: Factorial is obtained by multiplying that number to every other number below it. For example,…

Q: Given the following rational and irrational numbers,  order the numbers from least to greatest.…

A: Given rational and irrational numbers is 100      545      14      0.1111...      -2.5      51.

Q: Is the cube root of 7 a rational number? Is it a transcendental number? Is it a real number? Justify…

A: Cube root of 7 is not a transcendental number as x3-7 is a polynomial whose root is 71/3. Now,…

Q: (a) Suppose we want to test whether or not the number 217 is prime. List the minimum amount of…

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Q: 3. Consider the numbers A and B below. A = 235 × 512 × 7²1 B = 223 x 37 x 732 (a) Consider the…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: If a rational number times an irrational number is

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Q: 6. Where is 50 + 5 located on a number line? a) between 7 and 8 b) between 8 and 9 c) between 9 and…

A: 50=7.075=2.23

Q: Why do these rational numbers have terminating decimal? 1/30, 1/32, 1/40, and 3/60.

A: The number is said to be terminating if its denominator is in form of 2x5y. Simplify each number and…

Q: Find the indicated real nth root(s) of a. n = 4, a = -81 O +3 -/3

A: This question is about nth real roots of numbers

Q: 1) Give an example of a rational number AND an irrational number.       What is the difference…

A: (a) A rational number is of the form pq where p and q are integers where q≠0. The numbers that…

Q: Write a detailed proof for the statement: Between every two rational numbers there exists an…

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Q: Suppose you divide a natural number n by a positive rational number less than 1. Will the answer…

A: Take a rational number x=p/q such that x belong to (0,1)

Q: Consider the set of rational numbers under the operation of addition. What is the inverse of 9?

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Q: . Find the remainder when 15 + 25 +35 + ... +985 +995 +1005 is divided by 4.

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