       Reals and Equal

• To: mathgroup at smc.vnet.net
• Subject: [mg62013] Reals and Equal
• From: dh <dh at metrohm.ch>
• Date: Wed, 9 Nov 2005 03:45:27 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,
Comparing real numbers can give you considerable headache if you do not
exactly know how it works.

The Help says:
"Approximate numbers are considered equal if they differ in at most
their last eight binary digits (roughly their last two decimal digits)"
This is not quit right, as you can convince yourself:

(my Mathematica version: 5.1 for Microsoft Windows (October 25, 2004))

a=1./2;
b=1/2^47;
(a+b)== a
gives True

However,
a=1./2;
b=1/2^47 + 1/2^53;
(a+b)== a
gives False

that is, if two reals differ  only in the 7th last bit, they are
considered equal (and e.g. "<" gives False). However, if in addition the
last bit also differs, they are considers not-equal.

Can anybody give a reason for this strange behaviour.

sincerely, Daniel

```

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