Fractions. Help sought please.

[Salad Dodger]

Respect to you Compo for signing up for the maths course. Best of luck with it!

 

[twentysix by twentyfive]

Tell me about it!

No, I don't mean actually tell me about it ... I mean I have a minus sign on my bank statement too!

It's the way of the world Colin

 

[annedonnelly]

Compo, if it helps think about your fractions as pieces of cake or pizza - you cut the cake into 4 pieces - each is a quarter. Take away 3 quarters and you've a quarter left. In your case you had half a cake to start with (2 quarters ) and took away 3 quarters so you're left with minus 1 quarter (or -1/4).

Obviously you need more cake...

 

[marinyork]

Well it is real - the electric charges on quarks and anti-quarks are -1/3 and -2/3 in units of the proton charge. There's almost certainly other real examples - I just can't think of them at the moment.

Reality can be quite strange

Nice point.

If you take colo(u)r states of gluons you get a lot of 1/√2s and a 1/√3 and even anticolo(u)rs (and i). The fine structure constant with 'natural' units is e²/4π where e here is electric charge. Talking of quarks if you want more negative fractions there is weak isospin which has -1/2s in there.

 

[marinyork]

[QUOTE 2722065, member: 9609"]

Any body got a better explanation, my little brain is approaching meltdown[/quote]

A certain view would be that some things it makes 'sense' to talk about there being negatives and others it doesn't. So the problem you describe is a vector for which it makes 'sense' to talk about negative things. The out of the box example people would usually give would be that mass cannot be negative whereas weight most definitely can. Often various courses like school physics like to make the distinction between 'vectors' and 'scalars'. One of the problems with this is that at school they don't explain the further ideas behind this classification, 'it's just like that', but in a way it's actually a very important distinction that plays out in higher level physics. If you think the positive multiplied with negative rule is weird you should see what it is like combining polar and pseudovectors! You might say well what the smeg has that got to do with anything, but it turns out many things as unimportant as the magnetic field are pseudovectors.

As Thom rightly says, the important idea is the commutative property. Get rid of the commutative property and interesting things happen...

 

[ayceejay]

Compo, if it helps think about your fractions as pieces of cake or pizza - you cut the cake into 4 pieces - each is a quarter. Take away 3 quarters and you've a quarter left. In your case you had half a cake to start with (2 quarters ) and took away 3 quarters so you're left with minus 1 quarter (or -1/4).

Obviously you need more cake...

This is the kind of illogical carrying on I was talking about. "you cut the cake into 4 pieces" - if my brother was in charge of the cutting there would be two big pieces and two small pieces, after he took away the two big pieces there would be a quarter of the cake left which was my share according to him - this is known as big brother divvying and is what the real world is like beyond polar and pseudovectors, flavours I don't like anyway.

 

[Archie_tect]

Three fisherman decide to divide their day's catch equally the next morning, then go to sleep. Next morning, the first to wake up notices that the number is not exactly divisible by three. But he throws one back in the sea which makes the remainder a multiple of three, takes his third share, and leaves. The second to wake up doesn't realise the first has gone. He also notes that the number now remaining is not divisible by three, but he throws one back, and is then able to take exactly one-third of those remaining and leave. Likewise the third fisherman.

Q: what is the smallest initial number of fish there could have been?

That's daft... there aren't any fish swanson. If the mathematician has to make non-existent fish up then he's no use to fishermen. Simples

 

[Longshot]

Just in case you were wondering, there's also a negative infinity as well as its better known cousin, positive infinity.

 

[marinyork]

Just in case you were wondering, there's also a negative infinity as well as its better known cousin, positive infinity.

See negative temperature/spin states/population inversion .

 

[threebikesmcginty]

See negative temperature/spin states/population inversion .

I think our washing machine's got that setting.

 

[annedonnelly]

Just in case you were wondering, there's also a negative infinity as well as its better known cousin, positive infinity.

Isn't there also an infinity that's bigger than regular infinity? I need to read up on that one sometime.

 

[Archie_tect]

Nothing can bigger than infinity... surely

 

[PeteXXX]

Nothing can bigger than infinity... surely

infinity+1?

 

[Andy_R]

infinity = (n)infinity+1 where n = the number of infinities you already posess

 

[marinyork]

Nothing can bigger than infinity... surely

I'm awful at explaining things but this line of thinking was a very famous problem in mathematics a bit over 100 years ago. There are the integers which in common language have an infinite size and there are the real numbers which also have an infinite size but are 'bigger' despite both of them being called infinite. The question was are there any other infinities between the two. This problem is called the Continuum Hypothesis which they spent decades arguing about and then decided that they were asking the wrong question and "invented" a whole load of other stuff instead. Related to this is the rather head banging idea, to quite a few people, of something called the Axiom of Choice or as an ex put it, how can a load of mathematicians spend such a long time arguing about a concept so ridiculous with such a crazy name.