Feb 28, 2010 · By the sounds of it, he was disputing between peers whether 1/0 is infinite or undefined. This is obviously indicating that they're using a number system where the norm was to simply state 1/0 is undefined, but 1/0 can also be seen naturally as infinite by the sloppy use of limits in calculus as you've said.

Dec 19, 2021 · But if x is infinitely smaller, example 1/0.1, 1/0.01.., then it tends to infinity again. So 1/infinity tends both to zero and infinity. So i guess you can call it undefined.

Mar 26, 2003 · 1/infinity =0 There is no need to play games with it. Infinity is a carefully defined extension of the real number system. since it is not a real number all operations involving infinity and the real number system are defined.

Jul 8, 2005 · With the real number line. 0 is before -1 and 1. Both zero, and infinity are undefined. How does 0 touch infinity. Both are the same value, and start at 0, so for there to be infinity either infinity starts from infinity, or infinity starts from 0. In fact …

Oct 9, 2023 · Well, that could be treated that way, but practically in the approach I was taught, having 1/x limit equal to infinity just meant that the absolute value of ##\frac{1}{x}## may be made arbitrary large in a small enough neighborhood of x=0. That is, in that approach it was not the case that there was only one "infinity", but the following three ...

Jul 8, 2008 · This really means you just need to be careful. There may be a removable singularity (eg sin(x)/x at x=0), a singularity like 1/x or 1/x^x at 0, or an essential singularity (such as log(z) at 0), when viewed as a function from C to the extended complex plane. The nature of the singularity may tell you something useful.

Oct 6, 2023 · 1/ infinity = 0, but this seems a simplification. I understand the mathematics that 1 divided by infinity is virtually zero and so equals zero. I look on the internet and that is the answer that I get.

Oct 5, 2008 · Homework Statement Find a continuous surjection from [0,1) onto [0, infinity) Homework Equations The Attempt at a Solution I have only been able to come up with one mapping but then I realized it did not work. Any help would be appreciated.

Nov 14, 2003 · No, 1/infinity is not equal to 1/0 and -1/infinity is not equal to 1/0. Sometimes you will see "1/infinity= 0" (not 1/0 !) or "1/0= infinity" but those are again "shorthand" for more complicated limit statements (and which I prefer not to use because they are so easily misunderstood).

Dec 7, 2004 · Calculus, on the other hand, which has been essential to physics since Newton, deals infinities all the time and in that field 1/0 = infinity, and reciprocally, 1/infinity = 0. Calculus does not provide for adding and subtracting infinities, only multiplying and dividing them, but in Quantum Physics, infinity - infinity does equal 0.