Recent content by Aeneas

Many thanks tiny-tim!

If Un+1=Un + d defines an arithmetic progression, and Un+1 = kUn defines a geometric progression, is there a name for a progression defined by Un+1 =KUn + d? Thanks.

If you differentiate the formula for the volume of a solid sphere, 4/3 \pir3, you get 4\pir2, the formula for the surface area. This seems to make sense, as, onion-like, the sphere is made up of successive surface areas, so the rate of change will be the surface area for any given r. If you...

Thanks for those replies. Can you use "exponentiation" as a noun, to go with "addition" and "multiplication" for example, to generally describe the general process of raising one number to the power of another, then, or should it be reserved for raising e or some other number to the power of x...

Can you please help me sort out my terminology? Are 'power', 'index' and 'exponent' exact synonyms, even thogh they tend to be used in different contexts? If a^x gives 'exponential growth' is the growth described by x^a also properly called 'exponential'? If not, what is it called...

As far as I can make out, there is no formula available to calculate the number of free n-polyominoes, only bounds. Can you please confirm whether this is the case. If there is a formula, could you please point me to it. If there is not, is the problem just unsolved or has it been shown in some...

Thanks for that, but I do no fully follow the replies in the link. One reply says that when you write p^{a/b}, a and b must be mutually prime. The demonstration that p^{a/b}= \sqrt[b]{p^{a}}seems to work whether they are or not. e.g. p^{a_{1}/b} X p^{a_{2}/b} ...X p^{a_{b}/b} = p^{ab/b}=...

Could someone please sort out this contradiction which must come from some very basic error - but where and which error? If you raise -3 to the power of 1/2, this gives the square root of -3 which has no real value, but if you raise it to the power of 2/4, you are finding the fourth root of -3...

Sorry KTM. By 'original posts' (I missed off the 's') I meant the ones at the start of the thread, not yours. The point I was trying to make is that it is a common misconception that Euclid's proof rests on multiplying together any 'assigned multitude of prime numbers' (Heath) and adding one to...

Euclid did it in Book 9, Proposition 20 - but it is often stated slightly wrongly as in the original post. Multiplying the first n primes and adding 1 gives EITHER a new prime OR a composite number having a prime factor not in the original list. This proves that the number of primes is infinite.

Exactly! It would be represented as a horizontal line, so you cannot tell whether the person is at rest or walking along an arc of a circle which has his starting point as its centre. This is part of my objection to these 'distance from' graphs, particularly as they are still cropping up in...

Sorry I didn't make it clearer. The kind of graphs I'm talking about are ones where 'Distance from a starting point' is plotted against time - as opposed to graphs where 'distance travelled' is plotted against time. The first can obviously go back down to y = 0 as you return home, the second can...

"Distance from..." graphs At G.C.S.E level (England), there are still some questions knocking around about "distance from.." graphs as opposed to "distance traveled .." graphs. The first can go down as well as up, as the person returns to their starting place, while the second can only...

Many thanks Eighty, EnumaElish and fopc. Eighty's answer, then, seems to be saying that the two-way arrow is O.K.here, and that the book is wrong to say that it is not?

Implication There were no preliminary steps; it was just an answer to an exercise. I am aware of the a = b = 0 possibility but 2x+1 = x does not allow this. I think what I'm really asking is this: can one statement imply a second by virtue of implying a third? Can 2x+1 = x imply that...