Anis a topological subspace of such that given any pointn-dimensional (real) manifoldxin there exists a real number (depending onx) such that the open ball is homeomorphic to .

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Monox D. I-Fly wrote:a nickel is a tenth of a dollar and a dime is a twentieth of a dollar.

Are you sure?

That's what Google said.

]]>Inherent love for numbers!

]]>Lucas,

you mention that pi divided by 10000..... million is proof. However, then its not pi. The value of pi is changed. You are dealing with the unaltered value of Pi, that is in the order of 3.14159......

so I do not think your disproof is correct

The disproof is correct (as long as he divides by 10^(10^6) rather than 10^6). The product of a (non-zero) rational number with an irrational number is always irrational, and the statement in question was about irrational numbers, not π.

]]>ganesh wrote:Whats so special about the TN

1.444667861..................??????Is it known if this number (i.e. e^(1/e)) is transcendental?

It has not been proven to be transcendental, I don't think.

]]>Better yet, "the rest is left as an exercise for the reader".

]]>For example, isomorphisms are easy, they are what you use to say that two groups are equal. But is there a way we can use that kind of language with homomorphisms?

Aside from preserving an algebraic structure, there are ways in which such algebraic structures can be visualised. One of my favourite examples includes homomorphisms of directed graphs.

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What did you think of my sum answer in reply to your question?

]]>The problem with mathematics is that it is inherently contradictory/paradoxical.

Consider this, before we can think about something like e.g a math problem....we need time, say 1 second. But 1 second is composed of an infinite amount of fractions of a second. So before we can pass the threshold of 1 second, we first have to pass all these smaller fractions of time....this is an impossibility due to the infinite amount of fractions of time between the zero moment and 1 second...so no thought is possible mathematically.

In fact life is not possible...since there was no time to create it.

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