MathsIsFun

Good on ya, BigMoosie! We WERE having fun. I was looking forward to the next installment, and then it got closed. I think that playing with the concept of infinity is part of being human. Just because some of you may be tired with it, doesn't mean others are. By discussing and sharing ideas, we grow and learn, and who knows, someone may achieve an important insight here.

OK, we can test which is best. Say you are estimating your supermarket bill. Round off everything to the dollar, add em up and see how close you get to the answer. Pretend they are all negative numbers, in fact they are! If you have -49.5 becoming -49 then there will be 6/10 (0,1,2,3,4 and 5) being made closer to zero vs 4/10 (6,7,8,9) being made further from zero. This should bias your estimate. So, it is better to have 5 joining 6,7,8 and 9.

It is all about fairness. Gotta have the same number of players on each team. 0,1,2,3 and 4 are on team "down" 5,6,7,8 and 9 are on team "up" So -49.5 joins its fellows -49.6, -49.7, -49.8 and -49.9

Awww, don't ruin the fun ... this is wonderful stuff. I take the point that infinity is not a real number, but that shouldn't stop us playing with it in relation to real numbers. So, let us slice that apple into infinite pieces and then add up all the pieces to see if we get the apple back again! Yes, we cannot REALLY slice it up like that, but in our minds we CAN.

For all *practical* purposes x/infinity (where x is finite) is indistinguishable from zero, BUT to use it for *mathematics* it needs to be considered infinitesimal. Say we want to calculate the area under a curve, let's divide it into infinite slices and sum up the little mini-areas. The area is the height by the width. The height is the value of the function at that point, and the width is ... ummm ... zero. Oh THATS easy, the area is zero. On second thoughts, lets's make x/infininity=zero. Calculus becomes a lot easier

If x is finite, then x/infinity is "infinitesimal". And, I agree that infinity/infinity is indeterminate.

It is BODMAS, BIDMAS, BEDMAS, and even PEMDAS depending where you come from! The second term means order/index/exponent or whatever you want to call that thing where you raise something to a power. Multiply and Divide are supposed to rank evenly and so are performed left-to-right in the absence of any other information. I have a little page on it here: http://www.mathsisfun.com/operation-order-bodmas.html