How we can understand the following answer:
1.01^365=37.78343
0.99^365=0.025518
The difference is just 2% between two numbers.
How much error and uncertainity is produced because of numerical numbers??
Why we focus about uncertainity and error while our numerical numbers can produce very big error?
Let us share and discuss this matter.
Please stop thinking yourself is highly educated and other are not.
Publish all paper which has the basic requirements, nobody can judge 100% of work.
It is a total different issue the first sequence
an=(1.01)^n (which is ascending, non converging)
with the second one
bn=(0.99)^n (which is descending and converging to zero)
Elementary Calculus...
Dear Demertris,
Thank you so much for your nice answer, but i really think it is not only descending and ascending calculus it is real numeric problem.
Dear Raed, you're quite right when you say ... numerical numbers can produce very big error (usually as a result of accumulation of unavoidable roundings). We should not trust blindly in every computer generated result. That is why interval computations were invented (see Wikipedia if you don't know this term) some ~60 years ago. In your particular case I have obtained:
1.01^365 is in interval [37.783434332887281, 37.783434332887283], and
0.99^365 is in [2.551796445221124E-02, 2.551796445221126E-02]
thus your own results seems quite correct. The function f(x) =x^365 (power function, not exponential!) is increasing (and quickly accelerating its growth when its non-negative argument increases). Enough to check: df/dx(0) = 0, while df/dx(1) = 365*364 = 132860. Convinced?
Thank you for your nice answer. 1^365=1
0.99^365=0.0255
0.99=1 am i right?
So why?
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