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Re: Bug 1+4/10
*To*: mathgroup at smc.vnet.net
*Subject*: [mg120107] Re: Bug 1+4/10
*From*: Bill Rowe <readnews at sbcglobal.net>
*Date*: Fri, 8 Jul 2011 04:55:01 -0400 (EDT)
On 7/7/11 at 7:32 AM, slawek at host.pl (slawek) wrote:
>If Mathematica answer that a == b is true, then Mathematica should
>also answer that N[a] == N[b] is true. It is trivial.
Agreed. And Mathematica does this using your example, i.e.
In[2]:= N[1.4] == N[1 + 4/10]
Out[2]= True
>You can, poor boy, check that 1.4 == 1+1/4 gives True, but N[1.4,
>30] gives different result than N[1+1/4, 30] .
You need to understand/learn the difference between
N[1.4] an identity operation, i.e.
In[4]:= 1.4 === N[1.4]
Out[4]= True
and
N[1.4, 30] another identity operation, i.e.
In[5]:= 1.4 === N[1.4, 30]
Out[5]= True
In[6]:= Precision[N[1.4, 30]]
Out[6]= MachinePrecision
and
N[1+4/10] an operation that decreases information
There is a very large set of values for x such that N[x] will be
1.4. Specifically,
N[1.4 + a $MachineEpsilong]==N[1.4]
will return true for any a such that Abs[a]<1
Since, all of these are equally valid choices, it would be
incorrect for Mathemtica to select one over all others.
Undoubtedly, this is why N[1.4, 30] is an operation that does nothing.
In short, N is not intended to increase the precision of a
number. There is no universally valid way to increase numerical
precision. Any attempt to do so requires creation of new
information which can be done in a large variety of ways.
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