State true or false -3 > -13

UkusakazaL 2021-03-09 Answered
State true or false -3 > -13
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faldduE
Answered 2021-03-10 Author has 109 answers
We know that negative number which is closer to zero is bigger. If magnitude of a negative number is less than magnitude of other negative number then negative number having less magnitude is greater. (Here, magnitude means distance of number from zero). Here, magnitude of -3 is 3 and magnitude of -13 is 13. We know, 3<13 . Therefore, -3>-13. Hence, given statement is true.
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Can we say that 2 = 2 / ( 2 / ( 2 / ( ) ) )?
We have
ϕ = 1 + 1 ϕ = 1 + 1 1 + 1 ϕ = 1 + 1 1 + 1 1 + 1 ϕ =
(with ϕ being the Golden Ratio)
Which gives us the confirmed infinite fraction
ϕ = 1 + 1 1 + 1 1 + 1
We also have
2 = 2 2 = 2 2 2 = 2 2 2 2 =
So by analogy we can deduce that
2 = 2 2 2 2
The sequence ( a n ) n Z + such that a 1 = 2 , a n + 1 = 2 a n gives lim n + a n = 2 , so indeed the representation should be correct.
Everywhere on the Internet that I see a continued fraction of 2 , it is
2 = 1 + ( 2 1 ) = 1 + 1 1 + 2 = 1 + 1 2 + 1 1 + 2 = 1 + 1 2 + 1 2 + 1 1 + 2 =
Why haven't I seen the representation 2 = 2 / ( 2 / ( 2 / ( 2 / ) ) ) mentioned, and see the above used instead? Is something wrong about my representation?
I would say it isn't mentioned because it is not useful: you cannot approximate 2 using the representation, unlike you can using the above one (which you can do by removing 1 1 + 2 n any member).