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Igoryamba
2 years ago
10

Which kind of number is more common: even numbers or odd numbers?

Mathematics
2 answers:
Ray Of Light [21]2 years ago
6 0

Answer:

Can someone explain? Interestingly, there are the same number of odd numbers as even numbers. Because they can have a one-to-one mapping with the natural numbers, they each set is countably infinite. There are countably infinitely many even integers

Nostrana [21]2 years ago
5 0
First things first - there are an infinite number of both even numbers and odd numbers.

It's important to realize that ∞
∞
(infinity) is not a number. Therefore it doesn't really make sense to talk about the "number" of even or odd numbers, or to write statements like even+1
E
e
v
e
n
+
1
, because that's assuming that even
E
e
v
e
n
is a number that you can sensibly add 1
1
to.

However, perhaps surprisingly it does make sense to ask if there are more even numbers than odd numbers. That is, you can compare two infinite quantities, or compare a finite quantity and an infinite quantity, even if you can't meaningfully add and subtract infinite quantities.

They way we define more, less and the same for infinite quantities is as follows. For two collections
A
and
B
(say
A
are the even numbers and
B
are the odd numbers) we say that

If you can associate every item in
A
with a unique item in
B
, and vice versa, then
A
and
B
are the same size.
If you can associate every item in
A
with a unique item in
B
, but not vice versa, then
B
is bigger than
A
.
If you can associate every item in
B
with a unique item in
A
, but not vice versa, then
A
is bigger than
B
.
In your case, you can associate every even number
n
with the odd number +1
n
+
1
, and you can associate every odd number
m
with the even number −1
m
−
1
(assuming 0 is even) so therefore there are just as many odd numbers as even numbers.

This can lead to seemingly paradoxical results, because e.g. you can associate every whole number
n
with the even number 2
2
n
, and every even number
m
with the whole number /2
m
/
2
, so there are just as many even numbers as whole numbers, even though the even numbers are a subset of the whole numbers.
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What the value of 6(2b-4} when b=5
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8 0
2 years ago
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Evaluate: 11 + sqrt(-4 + 6×4÷3)
Murrr4er [49]

Answer:

11+\frac{2\sqrt{15}}{3}

Step-by-step explanation:

11 + \sqrt{(-4 + 6\times4\div3)} \\\\11+\sqrt{\frac{-4+6\times \:4}{3}}\\\\\sqrt{\frac{-4+6\times \:4}{3}}=\frac{2\sqrt{5}}{\sqrt{3}}\\\\=11+\frac{2\sqrt{5}}{\sqrt{3}}\\\\\frac{2\sqrt{5}}{\sqrt{3}}=\frac{2\sqrt{15}}{3}\\\\=11+\frac{2\sqrt{15}}{3}

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Money in a bank triples every 10 years. If $100 is deposited today, what will its value be after 40 years? PLEASE SHOW ME STEP B
LenKa [72]

Answer:

d) $8,100

Step-by-step explanation:

Given information:

  • Money triples every 10 years
  • Initial deposit = $100
  • Number of years invested = 40 years

If the money triples (multiplies by 3) every 10 years,
then in 40 years time it will triple <u>4 times</u>, as 40 ÷ 10 = 4

⇒ Account balance after 40 years = $100 × 3 × 3 × 3 × 3

                                                         = $100 × 3⁴

                                                         = $8,100

<u>Proof</u>

In 10 years time the balance of the account will be:

$100 x 3 = $300

In another 10 years time, the balance of the account will be:

$300 x 3 = $900

In another 10 years time, the balance of the account will be:

$900 x 3 = $2700

In another 10 years time, the balance of the account will be:

$2700 x 3 = $8100

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Answer:

(a) Two x plus eight is greater than negative four

(b) x > -6; number line would be an open circle at -6 and the line pointing in the positive direction to be shaded

Step-by-step explanation:

(a)

Note first that the inequality sign ">" means "greater than", so 2x + 8 > -4 in written language is:

<em>Two x plus eight </em><em>is greater than</em><em> negative four</em>

<em />

(b)

We solve this just like how we'd solve it if it were 2x + 8 = -4: isolate the variable first.

Subtract 8 from both sides:

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Divide by 2:

x > -12/2

x > -6

So, the solution set is all numbers greater than -6.

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