<p>Any thoughts? Calculus AB teaches that it does, but what's the REAL (if any) answer?</p>
<p>In the real number system, that statement is meaningless as division is only defined for comparison between two different real numbes. there are other systems, but thats too much for now.</p>
<p>1/1000000000000000000000 is very close to zero. As a approaches infinity in 1/a, the number becomes infinitesimally close to zero.</p>
<p>yes, but when you are trying to find an asymptote or tangent line, you plug infiniti in and when the exponent on one is higher than the other, going back to 1/infiniti, then that solution makes the solution 0. So what can be said for that expression?</p>
<p>"infinity" is not a number, or at least not a real number. The statement 1/inf is meaningless. It can be used only as a shorthand for lim 1/x as x approaches infty.</p>
<p>It gets close to 0 but not quite.</p>
<p>its a limit problem. Infinity is not a number. It is an expression of the largest number out there. So, imagine 1/infinity as writing 0's from here to the edge of the universe, and then add a 1 at the end. That is pretty much 0. In math we just use it as 0 because the remainder doesn't matter. It doesn't affect the problem you are doing. So, when you divide 1/infinity, the answer is not exactly 0, but it is so small, that it is considered 0. What else would you consider it?</p>
<p>haha i just finished studying this in calculus. isn't it a l'hopitals rule or something.</p>
<p>you need to know that 1/infinity is 0 in order to be able to do l'hopitals rule. You need it for a lot of things in calculus. So people, don't argue because it is right and you will need it for a lot of things in math.</p>
<p>yes. it approaches zero..
but since "infinity" is "infinite," 1/infinity is same thing as zero.</p>
<p>This sounds like infinitesimals...</p>
<p>As tetrahedr0n and I have said, infinite is not a number in the real number system. It is entirely non-rigorous to treat infinte as such.<br>
As long as we are on that topic, many aspects of the calculus are extemely suspect i.e. infintesimals. </p>
<p>The calculus that they teach us in schools works, but well....</p>
<p>First off the notation is screwed up. dy/dx used both as a differential operator and a quotient of differentials? When you learn differential forms you will realize some stuff.</p>
<p>And yes - differentials. dx. What the heck is that? What does it mean to perform arithmetic operations with "infinitely small numbers" mean? What the heck is an "infinitely small number?"</p>
<p>Thank goodness for Abraham Robinson and non-standard analysis.</p>
<p>One last thing - an antiderivative is not an integral.</p>