deano8177 wrote:What's 1+1+2, first one back with the correct answer gets a free pint.
I'm gonna think outside the box and say 112? This thread has opened a HUGE can of worms lol.
maths question
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CrosbyRules
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harry2 wrote:Technically it's infinity.
For the most part this is true Harry, anything divided by 0 is infinity. There are two exceptions to this rule, which is when the numerator (the number on top) is zero or infinity itself. In these scenarios it is important how the zero or infinity are arrived at.
It is interesting to learn that when you divide these amounts by zero, the answer is not always the same. You need to break down how quickly the zero or infinity is arrived at and this will determine the final outcome.
For example, if the top 0 was arrived at by the inverse of the infinite series 1+1+............+1 or, 1/(1+1+...........+1)
And the denominator (the number on the bottom) was the inverse of the infinite series 2+2+............+2 it is clear to see that the zero in the denominator arrives at zero at twice the rate the zero in the numerator.
It is said here, that zero divided by zero tends to 0.5. The important part here is the tends to, or tend towards.
This topic was recently discussed on radio 2, with the mathematician not going into quite as much depth as she could have, leaving a slightly skewed view of the answer. In short, when you start dividing by zero, anomalies can occur.
Interesting to hear people's views on the original post.
Technically, a single value can't be assigned to a fraction where the denominator is 0 so the value remains undefined.harry2 wrote:Technically it's infinity.
"If only there were evil people somewhere insidiously committing evil deeds, and it were necessary only to separate them from the rest of us and destroy them. But the line dividing good and evil cuts through the heart of every human being. And who is willing to destroy a piece of his own heart?"
Quite correct blackmogu.blackmogu wrote:Technically, a single value can't be assigned to a fraction where the denominator is 0 so the value remains undefined.harry2 wrote:Technically it's infinity.
Another way to express it would be to say that as the denominator tended to zero, then the fraction as a whole would tend to infinity. e.g. if dividing by 0.1 there would be a large number, by 0.00001 a much larger number, by 0.0000000001 an even larger number.
When considering this however, it is always worth looking at approaching the limit from both sides. i.e. what would happen if the denominator was negative. At which point as we tended towards zero, the fraction as a whole would get larger and larger, however would be negative. (Importantly, here I am assuming that the numerator remains positive. As we all know if it was negative then that would give a different outcome)
Now, what'll really make you think (if you are interested in this kind of thing), is that there are an infinite number of infinities.
See http://en.wikipedia.org/wiki/Georg_Cantor
See http://en.wikipedia.org/wiki/Georg_Cantor
"If only there were evil people somewhere insidiously committing evil deeds, and it were necessary only to separate them from the rest of us and destroy them. But the line dividing good and evil cuts through the heart of every human being. And who is willing to destroy a piece of his own heart?"
Found this great explanation of why the answer is 41
[/quote]Just in case anyone's wondering why we do multiplication before addition, one explanation is that it's because of algebraic notation. Algebra helps to shorten mathematical sentences. For example, if you have 5 apples and 3 bananas, you could call that "5a + 3b". Now bear in mind that the expression "5a" actually means "5 x a" (or "apple" multiplied by 5 if you like), so the whole expression really means "5 x a + 3 x b". Now, if you did these operations (adding, multiplying etc) from left to right, you would get, after each stage, running totals of; "5a", then "5a +3", then a final answer of "5ab +3b". Unfortunately, the "5ab" part doesn't make sense, because there is no such thing as "five applebananas". Everybody, whether mathematically minded or not, understands that if you say "I've got 5 apples and 3 bananas, you mean "five lots of apples PLUS 3 lots of bananas". This statement is translated mathematically as:
"5 x a + 3 x b"
and the multiplications are carried out first, the additions last.
Mathematicians realised centuries ago that algebraic notation required multiplying to be carried out before adding and decided that there should be standard rules of precedence in operations when performing arithmetic. It was a natural decision to make multiplication take precedence over addition because it is consistent with algebraic notation and therefore less confusing(!!!)
Now, if you consider the following situation:
A person is given 42 scratchcards. He wins £40 on the first one, he then loses the next 40, then he wins £1 on the last one. How much money has he won altogether?
Clearly, he has used all 42 scratchcards and his total winnings are £41. (1 lot of 40, 40 lots of 0 and 1 lot of 1)
Now in order to write this down algebraically, you could consider the letters f, z and o to represent occasions where he won forty, zero or one pound respectively.
This then becomes:
1f + 40z + 1o
but we don't need the "1" in front of f and o, so it simplifies to:
f + 40z + o
but now, putting the values of f =40, z = 0 and o = 1 into the expression gives:
40 + 40 x 0 + 1
which was the question posed in the original post.
The introduction of algebra to this situation may seem like it's making it even more complicated, but it's the best way I can think of to illustrate the reason why the answer can only be 41.
