Vi Hart: 9.999… reasons that .999… = 1

When you went to grade school, were you taught that ‘it is impossible to divide by zero’?  Or, that ‘we do not divide by zero’, as Vi Hart claims in the video she was taught?

I only ask because where I went to grade school (the other side of the iron curtain), we were taught from the very beginning that anything divided by zero = infinity….

Interesting video.  Personally, the argument I find most convincing is the demonstration of equivalence because there is no number which is greater than 0.9999repeating and 1.0.

OK, now for a bit of philosoraptoring

What does the term ‘=’ mean:  is ‘equal to’ actually mean ‘the same’?  Or does it mean ‘equivalent’…

Or, indeed, does ‘the same as’ mean ‘the same’?

Would you get into a Star Trek type replicator-transporter?

One Response to “Vi Hart: 9.999… reasons that .999… = 1”

  1. derek Says:

    fun speculation but i am inclined to disagree with her reasoning.

    1. face value. a = a. 1 cannot be anything other than 1.

    2. 1/3 = .333… , but only because it cant be divided into 3 equally. theres a remainder, no matter how small it is. 6 goes into 21 3 times. logically, can we say 18 = 21? of course not.

    3. third, .999, as she said gets closer and closer, by decreasingly smaller increments, but NEVER approaches 1. there is no number “right before” 1 or any number, because how we categorize numbers is purely subjective in that way. her premises are correct but they do not reach her conclusion.

    Xanthippa says:

    This is what I was getting at with my philosoraptoring.

    It is not possible for 0.9999repeating to be identical to 1, because 0.999rep. is an irrational number while 1 is a whole number (as well as a natural number). Therefore, they cannot be ‘identical’ because each belongs to a different number set.

    They are, however, ‘equivalent’ in some aspects….in the way that when you see something which is ‘the same as’ something else, they are not ‘each other’ – or there would not be the need for comparison.


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