Ok. Got to thinking the other day…
If I have $100 and you have $1, then one can obviously say that I have 100 times more than you.
Now, if I still have the same amount and you’re flat-off-your-ass broke ($0) then how many more times money do I have than you?
See, I’m thinking: you can’t divide or multiply with 0, so the answer is “no answer”. But I want something more conclusive than that =)
I believe the answer is either infinity or approaches infinity.
You’re right – there is no answer – and that’s the most conclusive thing you’re going to get. Because if you multiply $0 by any number, you are still going to get $0.
Actually, for clarity and unambiguity, it would be better to say “I have 100 times as much as you.”
If you have $1 and I also have $1, then I have (one times) as much as you, not one times more.
If you have $1 and I have $2, I have two times as much (or twice as much) as you. “Two times more” could be interpreted to mean that I have $3: I have what you have, and then that much again, and then that much again: two times more than you.
Specifically, as his money approaches zero you approach infinitely times as much as him.
Gotcha
I did actually mean “x times as much as you”… just thought it sounded more grammatically correct with my version, without giving much thought to the content.
Thanks all the same, guys!
Right. Take the 100 and divide it by, say, an amount a. Then let a get smaller and smaller. You find that there is no number, no matter how large, as an answer that you can’t exceed by simply making a smaller.
Mathematicians would say that the ratio 100/a has no limit, or upper bound, as a approaches zero.
Division by zero is not allowed. How much more conclusive an answer do you want?
Wait just a minute now, a more conclusive answer is X/0 = NO! :rolleyes:
Stated a little differently, to say $100 is “x” times more than zero is a nonsense statement, since any number times zero equals zero.
you would have $100 more than me. since i have no money for you to multiply you can’t phrase it that way.
Since we are talking about money here I don’t think that those who are talking about limits (Joey P, flight, Joey P, and David Simmons) can’t be right. Money comes in discrete amounts, including a smallest unit, with the property that every other amount is a positive integral multiple of the smallest unit – meaning that it can be modelled by the natural numbers. When you talk about a limit as something approaches zero, you mean that it can become as small as you like without equalling zero. But you can’t do that with money. If 1 cent is the smallest unit, then when you reach 1 cent you can’t go any lower than that, except to take 0 cents; and of course 0 cents creates the can’t-divide-by-zero situation.
Sorry – I shouldn’t have mentioned Joey P there twice!
Doesn’t matter whether you’re using money (or any other countable item) or love as my Dad did when he asked Mom to marry him (or any other uncountable). The math is the same.
In a broader sense, there are lots of situations where you can’t say “twice as much as” even though there is a numerical measure.
EXAMPLE: Temperature yesterday was 32 F, and today it’s 16 F. You really can’t say “it’s twice as cold today as it was yesterday,” that doesn’t make any sense. (And, by the way, if you were measuring in Celsius, you’d have different numbers anyhow.)
EXAMPLE: I have $100 in assets and you have $10 debt. Can’t say “I have X times more than you.” Doesn’t make sense.
Right – yesterday was 0 C, and today is -9 C – so some above would argue that it is infintely colder today, because -9/0 is infinity.
Perhaps you’re talking about currency, certainly not about money. My bank is very happy to deal in very long decimal fractions when they compute my interest charges.
Right – the intermediate calculations can be to any desired degree of accuracy. However, when they get the final result (i.e., the amount in your account, or the total on your statement), they round it to the nearest cent. There’s no way that you can own 1/10 of a cent: you either own a cent (as a coin, or as a balance in an account), or you own nothing.
(Interestingly, there have been US postage stamps valued in fractions of a cent, e.g. the 16.7 cent popcorn wagon stamp. However, even then, they are always in multiples of 0.1 cents, so you still can’t get infinitesimally small values.)
And the limit process is merely an intermediate calculation to show that division by zero does not produce a number that will serve as an answer to the OP question, and in fact division by zero will never produce a number under any circumstances.
In practice I can’t divide a circle into an endless number of infinitesmal pieces in order to find its area. But I can do it in my imagination just as I can imagine that money comes in infinitesmal increments. In the mathmatical model we aren’t dealing with money, we are dealing with numbers.
Yes, but what kind of numbers? You seem to be arguing for real numbers, but my contention is that you model money on the natural numbers, equating the number 1 with the basic unit of currency (which is 1 cent in US currency). (This only accounts for money as assets: to model debts, you need to bring in negative integers). Yes, in the real world you can have concepts like “5% interest per annum, compounded daily” – but again in reality, that’s only a simplification of the rule, because at some stage in the calculations you have to round an intermediate result to the nearest cent.
And the reason why you can’t divide by zero is nothing to do with limits or infinitesimal amounts of money: it’s because when you multiply any amount of money by zero, you get $0.00.
The result of dividing a number by zero is not infinity. Division by zero is undefined.