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AlekseyPX
3 years ago
9

There is no smallest positive rational number because, if there were, then it could be divided by two to get a smaller one. EXPL

AINED
Mathematics
1 answer:
Gennadij [26K]3 years ago
3 0

Answer:

Since a/2⁽ⁿ ⁺ ¹⁾b <  a/2ⁿb,  we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.

Step-by-step explanation:

Let a/b be the rational number in its simplest form. If we divide a/b by 2, we get another rational number a/2b. a/2b < a/b. If we divide a/2b we have a/2b ÷ 2 = a/4b = a/2²b. So, for a given rational number a/b divided by 2, n times, we have our new number c = a/2ⁿb where n ≥ 1

Since \lim_{n \to \infty} \frac{a}{2^{n}b } = a/(2^∞)b = a/b × 1/∞ = a/b × 0 = 0, the sequence converges.

Now for each successive division by 2, a/2⁽ⁿ ⁺ ¹⁾b <  a/2ⁿb and

a/2⁽ⁿ ⁺ ¹⁾b/a/2ⁿb = 1/2, so the next number is always half the previous number.

So, we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.

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8 0
3 years ago
Read 2 more answers
A Triangle has an area of 36cm^2. The base and height are scaled by a factor of 5. What is the area of the resulting triangle?
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Answer:

Area of resulting triangle  will be 900 cm^2.

Step-by-step explanation:

When sides of  any polygon if scaled by a factor of k

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5 0
2 years ago
The sum of four consecutive even integers is 256. what are the numbers?
Naily [24]

Answer:

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Step-by-step explanation:

Let the least even number be denoted by x. The sum of the four consecutive even numbers would be:

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First, simplify. Combine all like terms:

x + x + x + x + 2 + 4 + 6 = 256

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Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, subtract 12 from both sides of the equation:

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~

7 0
2 years ago
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