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#2 2011-08-20 20:20:36
- bobbym
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Re: Show that (413)^(1/3)>6+3^(1/3)
Hi;
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#4 2012-10-13 22:40:04
- Agnishom
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Re: Show that (413)^(1/3)>6+3^(1/3)
Hi Bobbym,
Is it okay to start with the thing we are trying to prove?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65
#5 2012-10-13 22:48:13
- bobbym
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Re: Show that (413)^(1/3)>6+3^(1/3)
Hi;
This is the problem:
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#6 2012-10-14 01:22:40
- anonimnystefy
- Real Member
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Re: Show that (413)^(1/3)>6+3^(1/3)
Hi bobbym
I think what Agnishom wanted to ask you is whether it is okay to start the proof with what we want to prove and work our way to a true statement...
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#7 2012-10-14 01:29:10
- bobbym
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Re: Show that (413)^(1/3)>6+3^(1/3)
Hi anonimnystefy;
I missed that. I am sorry about that. Bob and I had a good discussion on that and it seems better to work backwards in that case. Even though they do work forwards a lot in inequality books.
Unfortunately, whatever brilliant idea I had about this problem 1 year ago, I can not remember it at all.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#8 2012-10-15 04:15:30
- engrymbiff
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Re: Show that (413)^(1/3)>6+3^(1/3)
Hm... I really cannot solve it, I have a vague memory of how I solved it last time but now I don't have a good clue of how...
#9 2012-10-15 22:55:57
- scientia
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Re: Show that (413)^(1/3)>6+3^(1/3)
I have a very weird solution; you probably won't like it but I'll have a go anyway.
Let .
Then because .
Let .
We find (just). It follows that since the quadratic function is strictly increasing for positive x.
The LHS is and so we are done.