A mathematician is one that...

[inertia]

A mathematician is one that

is obvious as that twice two makes four to you.

Lord Kelvin, physicist

(Mathematicians actually don't regard this formula (attributed to Gauss) as 'obvious'.)

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[Eightcrackers]

An engineer, a physicist, and a mathematician were on a train ride through Scotland, when the engineer looks out of the window and sees a sheep paddock.

"Oh, look," he says "Scottish sheep are black!"

"No," replies the physicist, "some Scottish sheep are black."


The mathematician sighs, rolls his eyes, and intones

"In Scotland, there exists at least one sheep, at least one side of which is black."

 

[inertia]

An engineer, a physicist, and a mathematician were on a train ride through Scotland, when the engineer looks out of the window and sees a sheep paddock.

"Oh, look," he says "Scottish sheep are black!"

"No," replies the physicist, "some Scottish sheep are black."


The mathematician sighs, rolls his eyes, and intones

"In Scotland, there exists at least one sheep, at least one side of which is black."

I'll bite. The matematician is assuming the indeterminate value theorem I presume.

Let m and M be the extreme values of a function f continuous in [a,b]. If m <= k <= M there is at least one x belonging to [a,b] such that f(x) = k.

For this to be true, f must contain all values in [a,b] such that f(x) will also include 1/2. ( half black, half white ) ?

The engineer is not going to over-engineer their responses.

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