4x^-1 = 7/8

[jawillwill]

I've completely forgotten how to do this sort of equation. Somebody fancy solving what x equals please? Ta.

[Lighthouse]

4/x = 7/8

 

Therefore x = 32/7

[dubai_phil]

Remarkable Co-incidence. I happened across this article only today which should answer your query regarding complex equations.

 

http://www.telegraph.co.uk/science/8118823/Large-cardinals-maths-shaken-by-the-unprovable.html

 

If someone else could actually explain what the heck it was on about I would be grateful

 

I though infinity was infinity, not an infinite number of infinities of infinite sizes

[Smirking_Saint]

Are you saying 4 x (X to the power of -1) = 7/8 ??

 

If so it is differentiation.

 

(f)4X^-1 = (4X^-2 = 7/8 )

Edited 10 November, 2010 by Smirking_Saint

[Lighthouse]

Is x^-1 not just 1/x or have I got that wrong? Haven't done this shizzle in years.

Edited 10 November, 2010 by Lighthouse

[Smirking_Saint]

Is x^-1 not just 1/4 or have I got that wrong? Haven't done this shizzle in years.

 

I think it is 4 times X to the power of -1

[Lighthouse]

I think it is 4 times X to the power of -1

 

Sorry, that should read 1/x

[scotty]

4/x = 7/8

 

therefore x = 32/7

 

are you saying 4 x (x to the power of -1) = 7/8 ??

 

If so it is differentiation.

 

(f)4x^-1 = (4x^-2 = 7/8 )

 

pmsl!!!

[Smirking_Saint]

Have we been done ?

[scotty]

I would have thought it was obvious.....

[Ludwig]

Remarkable Co-incidence. I happened across this article only today which should answer your query regarding complex equations.

 

http://www.telegraph.co.uk/science/8118823/Large-cardinals-maths-shaken-by-the-unprovable.html

 

If someone else could actually explain what the heck it was on about I would be grateful

 

I though infinity was infinity, not an infinite number of infinities of infinite sizes

 

I could explain a bit of it to you in layman's terms, but I can't help but know very little about what it means for the large cardinals (big infinities) to be having an effect upon arithmetic. I'm unsure as to why they seem to doubt the existence of large cardinals, as I was under the impression that Cantor proved that there is an infinite hierarchy of cardinals for infinity. I could tell you about Godel, but I don't see what that has to do with the 'large cardinals' other than to demonstrate the previously proved impossibility of proving the consistency of arithmetic. I might ask my tutor about this tomorrow, he must know more than I do.

[dubai_phil]

I could explain a bit of it to you in layman's terms, but I can't help but know very little about what it means for the large cardinals (big infinities) to be having an effect upon arithmetic. I'm unsure as to why they seem to doubt the existence of large cardinals, as I was under the impression that Cantor proved that there is an infinite hierarchy of cardinals for infinity. I could tell you about Godel, but I don't see what that has to do with the 'large cardinals' other than to demonstrate the previously proved impossibility of proving the consistency of arithmetic. I might ask my tutor about this tomorrow, he must know more than I do.

 

Will look forward to the reply.

 

While you are at it, can you just confirm that what the article is saying is that Fat Roman Catholic preachers have meant that my weekly budget for housekeeping doesn't add up?

[Ludwig]

Wait, Godel proved that there are 'unprovable' theorems, without making axioms inconsistent, but if you added an extra axiom then the set of axioms would become inconsistent as a result (I think) in order to prove what is desired. However this was all entirely theoretical and there was no concrete example of the insufficiency of the axioms of arithmetic, whereas this guy seems to be studying 'patterns' (boolean algebras? dunno much about them tho) and has found patterns that should intuitively (possibly) hold true, but are unprovable using the axioms of arithmetic without adding an axiom that claims that large cardinals exist and have an effect, which leads to some inconsistency. Maybe. Probably not though.

[Deppo]

Thanks for that Ludwig - really interesting stuff.

[Robsk II]

Wait, Godel proved that there are 'unprovable' theorems, without making axioms inconsistent, but if you added an extra axiom then the set of axioms would become inconsistent as a result (I think) in order to prove what is desired. However this was all entirely theoretical and there was no concrete example of the insufficiency of the axioms of arithmetic, whereas this guy seems to be studying 'patterns' (boolean algebras? dunno much about them tho) and has found patterns that should intuitively (possibly) hold true, but are unprovable using the axioms of arithmetic without adding an axiom that claims that large cardinals exist and have an effect, which leads to some inconsistency. Maybe. Probably not though.

 

I bet you read the dictionary before bed, you speccy spec spec.

[dubai_phil]

Wait, Godel proved that there are 'unprovable' theorems, without making axioms inconsistent, but if you added an extra axiom then the set of axioms would become inconsistent as a result (I think) in order to prove what is desired. However this was all entirely theoretical and there was no concrete example of the insufficiency of the axioms of arithmetic, whereas this guy seems to be studying 'patterns' (boolean algebras? dunno much about them tho) and has found patterns that should intuitively (possibly) hold true, but are unprovable using the axioms of arithmetic without adding an axiom that claims that large cardinals exist and have an effect, which leads to some inconsistency. Maybe. Probably not though.

 

OK so an Axiom is something made up to make maths work? Over here it's a mobile phone company.

 

Sounds so like Masterchef - Well Greg I just added an extra Axiom 'cos I know you love your puddings

[JackFrost]

The thread title looks like a text message written by someone very ****ed

[scotty]

I wish somebody would start a thread about the theory of an infinitely-expanding universe so we'd have something to really sink our teeth into.

[benjii]

I wish somebody would start a thread about the theory of an infinitely-expanding universe so we'd have something to really sink our teeth into.

 

Yeah, the kind of person who would do that would be a mo-****ing goddarn legend.

[Whitey Grandad]

The equation is ambiguous as written. It could be (4x)^-1 or 4(x^-1)

[angelman]

I gave up on maths when I learnt that the square root of -1 was i

 

Never used a complex number in the 20+ years since I last did it.

[Whitey Grandad]

I gave up on maths when I learnt that the square root of -1 was i

 

Never used a complex number in the 20+ years since I last did it.

 

You might have used one without knowing it.

[Smirking_Saint]

I gave up on maths when I learnt that the square root of -1 was i

 

Never used a complex number in the 20+ years since I last did it.

 

Its actually J

[Ludwig]

I gave up on maths when I learnt that the square root of -1 was i

 

Never used a complex number in the 20+ years since I last did it.

 

Complex numbers are defined as x + iy, where x,y are integers. Are you saying you haven't used any such number where y=0 (so basically any numbers ever)?

[toofarnorth]

http://www.wolframalpha.com/input/?i=4x^-1+%3D+7%2F8+

[Whitey Grandad]

Its actually J

 

But that would mark you out as an engineer, and hence the lowest member of society.

[jawillwill]

Just to confirm, it was meant to be (with no brackets anywhere):

 

4x(to the power of -1) = 7/8

[benjii]

 

cool

[Ken Tone]

Just to confirm, it was meant to be (with no brackets anywhere):

 

4x(to the power of -1) = 7/8

 

Then lightouse solved it for you correctly in the second post on the thread ie x =32/7 or 4 and 5/7.

 

x to power of -1 simply means 1/x. The equation is just set out as an an unnecessarily complicated way of writing 4/x = 7/8, which => 4 =7x/8 => 32 = 7x => x = 32/7.

 

This is not complicated stuff. I suspect that if you think it should be you are confusing it with dim distant memories of the much harder scenario where you get equations like 4^x = something. In that case you have to take logs of both sides.

 

Whitey Grandad, it is not ambiguous because it only needs brackets if it does mean (4x) all to the power of -1. As it is written, it unambiguously means 4 times just x to the -1. Remember BODMAS ?

[Dimond Geezer]

Brackets

Order

Division

Multiplication

Addition

Subtraction

 

I'm an Engineer.

 

BTW the answer is 42

[Ken Tone]

Brackets

Order

Division

Multiplication

Addition

Subtraction

 

I'm an Engineer.

 

BTW the answer is 42

 

Not bad for an engineer!

 

Nowadays mind you, they teach 'BIMDAS', Brackets, Indices, Multiplication, Division, Addition, Subtraction . I just assumed someone with the user name 'grandad' might prefer the old version!

Either way the multiplication by 4 comes after the power, ie after the index/order.

 

Quite why they've turned round the 'M' and the 'D' I don't know. It doesn't matter of course, as multipication and division are equal in rank, as are addition and subtraction.

 

It's amazing how many cheap calculators (including the one on my blackberry) give the incorrect answer of 54 to the sum 4+5x6, as opposed to the correct one of 34.

[Whitey Grandad]

Not bad for an engineer!

 

Nowadays mind you, they teach 'BIMDAS', Brackets, Indices, Multiplication, Division, Addition, Subtraction . I just assumed someone with the user name 'grandad' might prefer the old version!

Either way the multiplication by 4 comes after the power, ie after the index/order.

 

Quite why they've turned round the 'M' and the 'D' I don't know. It doesn't matter of course, as multipication and division are equal in rank, as are addition and subtraction.

 

It's amazing how many cheap calculators (including the one on my blackberry) give the incorrect answer of 54 to the sum 4+5x6, as opposed to the correct one of 34.

I prefer preciseness. Some computer algorithms will parse from left to right, others not, but brackets will always make sure. BODMAS was what they taught me in infant school in the 50s but that was superseded many years ago. I never did find out what the O stood for.

[Dimond Geezer]

Not bad for an engineer!

 

Nowadays mind you, they teach 'BIMDAS', Brackets, Indices, Multiplication, Division, Addition, Subtraction . .

 

I was taught BODMAS, I needed my 13 year old son to tell me what the hell BIMDAS was.

 

I I never did find out what the O stood for.

 

'O' was order, or to the power of, ie 3squared, is '3 to the order of 2'.

[Ken Tone]

I prefer preciseness. Some computer algorithms will parse from left to right, others not, but brackets will always make sure. BODMAS was what they taught me in infant school in the 50s but that was superseded many years ago. I never did find out what the O stood for.

 

See Dimond Geezer's post ..'o' for order as in power. They didn't explain that properly to you in infant school because you hadn't done powers by then! The modern BIMDAS is supposed to be easier to understand, with 'i' being index. But either way there is no imprecision. The rules of grammar of maths are just that ..rules ..clear and precise. They have never been superseded. Go wash your mouth out with soap.

Edited 11 November, 2010 by Ken Tone
My spelling is not as good as my maths!

[Whitey Grandad]

See Dimond Geezer's post ..'o' for order as in power. They didn't explain that properly to you in infant school because you hadn't done powers by then! The modern BIMDAS is supposed to be easier to understand, with 'i' being index. But either way there is no imprecision. The rules of grammar of maths are just that ..rules ..clear and precise. They have never been superseded. Go wash your mouth out with soap.

 

BODMAS/BIMDAS is just a particular convenient convention, not a universal Law of Mathematics and should not be automatically assumed if it is not specified. I had done powers but my teacher hadn't. Reverse Polish convention assumes a different priority and anyone who has progammed in FORTH will know all about that.

[Ken Tone]

BODMAS/BIMDAS is just a particular convenient convention, not a universal Law of Mathematics and should not be automatically assumed if it is not specified. I had done powers but my teacher hadn't. Reverse Polish convention assumes a different priority and anyone who has progammed in FORTH will know all about that.

 

As far as I am aware the rules summarised by BIMDAS have been universally acknowledged in Mathematics since the 16th or 17th century, when the index notation was first developed. It may well be that early Computing languages ignored this rule, but then that is Computing, not Maths. Computing is a world of its own, and of course only a very recent upstart one. It invented many of its own conventions because of the limitations of early technology and programming languages. However those conventions had and have no validity outside that enclosed specialist world, and by now have mostly faded away anyway as modern technology has caught up. Thank God that silly 1970's affectation of writing a zero with a line through it has declined for example. (Never heard of FORTH, but I had to learn ALGOL and a bit of FORTRAN btw. What a waste of time that was!)

 

Anyone and everyone should indeed assume BIMDAS applies to any mathematical expression, unless otherwise specified. Certainly the OP should absolutely definitely assume that 4x^-1 means 4 times x^-1, not (4 times x)^-1.

 

Makes a pleasant change having an argument over something esoteric on here rather than over fence-rattling and coin-throwing on the main site! Want a punch up behind the Kingsland over this? I'll bring the thermos flask if you bring the sandwiches.

[angelman]

Complex numbers are defined as x + iy, where x,y are integers. Are you saying you haven't used any such number where y=0 (so basically any numbers ever)?

 

I've not needed to make up an imaginary number in the past 20 years, no. As we know, it is impossible to have a square root of a negative number so they had to go and make one up instead.

 

From wiki:

A complex number is a number consisting of a real and imaginary part. It can be written in the form a + bi, where a and b are real numbers, and i is the standard imaginary unit with the property i 2 = −1.[1] The complex numbers contain the ordinary real numbers, but extend them by adding in extra numbers and correspondingly expanding the understanding of addition and multiplication.

Complex numbers were first conceived and defined by the Italian mathematician Gerolamo Cardano, who called them "fictitious", during his attempts to find solutions to cubic equations.[2] The solution of a general cubic equation in radicals (without trigonometric functions) may require intermediate calculations containing the square roots of negative numbers, even when the final solutions are real numbers, a situation known as casus irreducibilis. This ultimately led to the fundamental theorem of algebra, which shows that with complex numbers, a solution exists to every polynomial equation of degree one or higher. Complex numbers thus form an algebraically closed field, where any polynomial equation has a root.

The rules for addition, subtraction, multiplication, and division of complex numbers were developed by the Italian mathematician Rafael Bombelli.[3] A more abstract formalism for the complex numbers was further developed by the Irish mathematician William Rowan Hamilton, who extended this abstraction to the theory of quaternions.

Complex numbers are used in a number of fields, including: engineering, electromagnetism, quantum physics, applied mathematics, and chaos theory. When the underlying field of numbers for a mathematical construct is the field of complex numbers, the name usually reflects that fact. Examples are complex analysis, complex matrix, complex polynomial, and complex Lie algebra.

Complex numbers are plotted on the complex plane, on which the real part is on the horizontal axis, and the imaginary part on the vertical axis.

[Whitey Grandad]

As far as I am aware the rules summarised by BIMDAS have been universally acknowledged in Mathematics since the 16th or 17th century, when the index notation was first developed. It may well be that early Computing languages ignored this rule, but then that is Computing, not Maths. Computing is a world of its own, and of course only a very recent upstart one. It invented many of its own conventions because of the limitations of early technology and programming languages. However those conventions had and have no validity outside that enclosed specialist world, and by now have mostly faded away anyway as modern technology has caught up. Thank God that silly 1970's affectation of writing a zero with a line through it has declined for example. (Never heard of FORTH, but I had to learn ALGOL and a bit of FORTRAN btw. What a waste of time that was!)

 

Anyone and everyone should indeed assume BIMDAS applies to any mathematical expression, unless otherwise specified. Certainly the OP should absolutely definitely assume that 4x^-1 means 4 times x^-1, not (4 times x)^-1.

 

 

Makes a pleasant change having an argument over something esoteric on here rather than over fence-rattling and coin-throwing on the main site! Want a punch up behind the Kingsland over this? I'll bring the thermos flask if you bring the sandwiches.

 

The problems come when you try to write a mathematical expression using a computer keyboard, although there would still be ambiguity if you were to write 1/4x, hence I always think it is better to be precise and either explicitly state the convention or use brackets. As they say in 'Under Siege 2', assumption is the mother of all f'ups.

 

I found FORTRAN very useful in its time and even wrote a few cross-assemblers in it. It is ideal for Fast-Fourier transforms, and handles complex numbers well. ALGOL could get very esoteric and if you put a bracket in the wrong place it would change the whole operation.