The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Math Topics » discretemath

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: How does infinitesimal exist?
Replies: 21   Last Post: Jun 7, 2013 12:13 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ] Topics: [ Previous | Next ]

Posts: 132
Registered: 11/27/12
Re: How does infinitesimal exist?
Posted: Apr 11, 2013 10:08 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Completely wrong. It is not just that "the last digit is difficult to write", there is NO "last digit". A numeral such as 0.999... represents the sum of an infinite series: .9+ .09+ .009+ .0009+ ... That sort of series is handled, in general in Calculus but special cases are seen in "Pre-Calculus" or "Intermediate Algebra".

.9+ .09+ .009+ ... is, in particular, a "geometric series". It can be written .9(1+ .1+ .01+ .001+ ...)
which is of the form a(1+ r+ r^2+ r^3+ ...) with a= .9 and r= .1.

And, it can be shown that the sum is equal to a/(1- r).
(Not "approaching" that, the sum is EQUAL to it.)

Here, that would be (.9)(1- .1)= .9/.9= 1.

0.9999.... is exactly EQUAL to 1.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.