the_lone_wolf
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- Dec 16, 2004
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ah, i think i see what you're getting at, but i'm not really comfortable with it, for a couple of reasons:
1. in the context of the function y=1/x even if there's was a value of y for which y could equal 1/0 then you still could not call the funtion continuous, because the valuse of y as {-x -> 0} and {x -> 0} are not converging, they are diverging.
2. you said
... -2 -1 0 1 2 ...
then your proposal says that you can have this:
... -999 -999999999 -999999999999999999999999999 {your number} 999999999999999999999999999999 999999999 999 ...
which simply cannot happen, if you continue to subtract from a negative number it will never become positive, no matter how much to subtract. (to be pedantic by it's very defenition you would never even reach "infinity")
3. the definition "undefined" doesn't just apply to y=1/0, it also applys to other undefinable mathematical quantities such as y=log(0) - this function is not symetric in the way |1/x| is, any value of x for which x is equal to or less than 0 is undefined in the equation y=log(x) . our concept of "infinity" simply cannot be described by the language of mathematics, "infinity" is not a number, it's a nice way of saying the value which satisfies the equation is undefined.
i hope you can see what i'm trying to say here, it's difficult to get thoughts from head to screen at times
1. in the context of the function y=1/x even if there's was a value of y for which y could equal 1/0 then you still could not call the funtion continuous, because the valuse of y as {-x -> 0} and {x -> 0} are not converging, they are diverging.
2. you said
if small numbers can be represented on a numberline thus:The purpose of this is to show that numbers go in a circle instead of a line. Positive and negative numbers are connected downwards by the zero, while they're connected upwards by the number produced by deviding by zero.
... -2 -1 0 1 2 ...
then your proposal says that you can have this:
... -999 -999999999 -999999999999999999999999999 {your number} 999999999999999999999999999999 999999999 999 ...
which simply cannot happen, if you continue to subtract from a negative number it will never become positive, no matter how much to subtract. (to be pedantic by it's very defenition you would never even reach "infinity")
3. the definition "undefined" doesn't just apply to y=1/0, it also applys to other undefinable mathematical quantities such as y=log(0) - this function is not symetric in the way |1/x| is, any value of x for which x is equal to or less than 0 is undefined in the equation y=log(x) . our concept of "infinity" simply cannot be described by the language of mathematics, "infinity" is not a number, it's a nice way of saying the value which satisfies the equation is undefined.
i hope you can see what i'm trying to say here, it's difficult to get thoughts from head to screen at times