Irrational Integers :)

a1call · 2017-05-13, 18:38

(n/(sqrt(n+1)-1))-sqrt(n+1)

paulunderwood · 2017-05-13, 18:50

Integers are equal to a subset of the rationals. For example an integer n is equal to n/1.

a1call · 2017-05-13, 19:04

a=sqrt(3)-1=0.7321
2/a=2.7321

science_man_88 · 2017-05-13, 19:08

Quote:

Originally Posted by a1call

(n/(sqrt(n+1)-1))-sqrt(n+1)

if you plug in n=3 you get 1 as your answer 3/(sqrt(4)-1) - 2/1 = 3/1-2/1=1/1 = 1 in fact you can restate this as n/(sqrt(n+1)-1)+(n+1-sqrt(n+1))/(sqrt(n+1)-1) = (2n+1-sqrt(n+1))/sqrt(n+1)-1) which is rational any time n is one less than a perfect square.

paulunderwood · 2017-05-13, 19:18

While we're on the subject of irrationality: Show there is a rational number that is equal to an irrational number raised to the power of an irrational number.

a1call · 2017-05-13, 19:49

Quote:

Originally Posted by paulunderwood

While we're on the subject of irrationality: Show there is a rational number that is equal to an irrational number raised to the power of an irrational number.

I know that one.
It's good looking.

paulunderwood · 2017-05-13, 19:52

Quote:

Originally Posted by a1call

I know that one.

Give the answer please with the use of spoiler tags.

a1call · 2017-05-13, 20:04

I dislike the spoiler tags.

https://en.m.wikipedia.org/wiki/Euler%27s_identity

paulunderwood · 2017-05-13, 20:13

https://en.wikipedia.org/wiki/Irrational_number says "In mathematics, the irrational numbers are all the real numbers, which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers"

That page also gives the answer to the problem I set.

a1call · 2017-05-13, 20:13

It is safe to assume that no one alive today is likely to come up with that identity without knowing it already.

Hence, no point in using the spoiler tags.

a1call · 2017-05-13, 21:18

Quote:

Originally Posted by paulunderwood

https://en.wikipedia.org/wiki/Irrational_number says "In mathematics, the irrational numbers are all the real numbers, which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers"

That page also gives the answer to the problem I set.

Doesn't
https://wikimedia.org/api/rest_v1/me...5f572fbf8bb256

satisfy the problem you set?

2017-05-13, 18:38	#1
a1call "Rashid Naimi" Oct 2015 Remote to Here/There 4007₈ Posts	Irrational Integers :) (n/(sqrt(n+1)-1))-sqrt(n+1)

2017-05-13, 20:13	#9
paulunderwood Sep 2002 Database er0rr 111010011011₂ Posts	https://en.wikipedia.org/wiki/Irrational_number says "In mathematics, the irrational numbers are all the real numbers, which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers" That page also gives the answer to the problem I set. Last fiddled with by paulunderwood on 2017-05-13 at 20:45

2017-05-13, 20:13	#10
a1call "Rashid Naimi" Oct 2015 Remote to Here/There 3×5×137 Posts	It is safe to assume that no one alive today is likely to come up with that identity without knowing it already. Hence, no point in using the spoiler tags. Last fiddled with by a1call on 2017-05-13 at 20:14

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2017-05-13, 18:50	#2
paulunderwood Sep 2002 Database er0rr 3,739 Posts	Integers are equal to a subset of the rationals. For example an integer n is equal to n/1.

2017-05-13, 19:04	#3
a1call "Rashid Naimi" Oct 2015 Remote to Here/There 3·5·137 Posts	a=sqrt(3)-1=0.7321 2/a=2.7321

2017-05-13, 19:18	#5
paulunderwood Sep 2002 Database er0rr 3,739 Posts	While we're on the subject of irrationality: Show there is a rational number that is equal to an irrational number raised to the power of an irrational number.

2017-05-13, 20:04	#8
a1call "Rashid Naimi" Oct 2015 Remote to Here/There 3×5×137 Posts	I dislike the spoiler tags. https://en.m.wikipedia.org/wiki/Euler%27s_identity