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#1 2006-12-05 15:46:13

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Inequality Approximation Sign?

I know that an exact value uses '=' and an approximation uses '≈', but what is the sign for an inequality approximation. Is it like, </>/≤/≥ but with the '≈' beneath... or...? As an example, how do you write x < √(2) in decimal format to 2 decimal places?

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#2 2006-12-05 17:45:56

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: Inequality Approximation Sign?

Typically when you use less than, you don't want there to be any chance that it is greater than.  So there is really no reason for an "approximation".


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2006-12-05 21:53:46

MathsIsFun
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Registered: 2005-01-21
Posts: 7,711

Re: Inequality Approximation Sign?

I am struggling to think of an example where you want to say that something was

* Approximately less than
* Approximately greater than
* Approximately not equal to

However I imagine you could say that something was "Less than or approximately equal to"


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#4 2006-12-06 00:53:11

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Re: Inequality Approximation Sign?

Well I had this question asking what the optimal hours that a painter should work for were, and I got x > 420/11.5, which is equal to 36.521739... and I put x > 36.521739, should I leave all inequalities as exact values?

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#5 2006-12-06 07:51:44

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Inequality Approximation Sign?

Normally, an optimization problem has a unique solution.  If you get an inequality as a result, then typically you either aren't solving the problem properly, or you don't have enough information to.  Can you give us the problem?


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#6 2006-12-06 07:51:51

MathsIsFun
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Registered: 2005-01-21
Posts: 7,711

Re: Inequality Approximation Sign?

Less than approximately ... how about a single squiggle?

x > ~36.5


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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