Recent content by mathsman1963

My problem with the questions being asked in this thread is that they are not mathematical questions. If they have not already crossed the line they are getting dangerously close to number mysticism. Isn't there a post in this thread linking the decimal expansion of π to the number of new moons...

I was aware. It is painfully obvious, however, given that the left hand side of the equation is a sum of increasing positive terms, their total (whatever it may be) cannot be negative. Just because we often meet counter intuitive results in mathematics it does not mean we throw good sense out of...

Rest assured, 1+2+3+...≠-1/12.

Can John Baez' Crackpot Index be applied to mathematics?

What other arguments do you expect in mathematics? The truth of a statement follows logically from axioms.

Well... no. This has nothing to do with a definition of flatness and has nothing to do with the physical world. In Euclidean geometry 6 equilateral triangles equal a hexagon. This can be proved. That is the end of the story. If the proof does not supply you with enough of the 'why' that's too...

There is nothing special about 6 equilaterals making a hexagon it is simply one result of their properties. Why are you looking for more than is there?

I would heartily recommend an OU degree. The material is well presented and the modular nature of the coursework means you are revising as you learn so you are better prepared when you reach the examination. The minimum time needed for the degree is three years but in order to achieve that you...

Ignore the probability for the moment. If the third head occurs after at least eleven tosses what is the maximum number of heads that can have occurred in ten tosses?

The Goldbach Conjecture is easy enough to understand: every even number greater than 2 is the sum of two prime numbers. Easy to state, fiendishly difficult to prove.

the modulus of x equals x if x is non-negative and -x if x is less than zero. It does not equal ±x. The equation mod(x)=2 has the solutions x= ± 2

Apologies, I made a boo-boo. (I'm getting carried away with this Tex business.) The fraction should be \frac {am+c}{2^{l}mc} The numerator is clearly even but, as you say, there is no evidence for the factors of 2. If it could be shown that k can never equal l it would prove the...

What if k=l? Then we get \frac a b + \frac 1 n = \frac a{2^kc} + \frac 1{2^lm} = \frac {2^l(ma + c)}{2^{l}mc} The 2l s cancel to leave \frac{ma + c}{mc} even divided by odd.

There is a way of proving that all the harmonic numbers greater than 1 are fractions with an odd numerator and an even denominator. Consider the denominators 1, 2, ...,2k, ...,n where k is the largest power of 2 such that 2k is less than or equal to n. Remove the fraction with the 2k...

Not being of a philosophical disposition I would define a mathematical object as any object studied in a mathematical way by a mathematician.