Motorola M500 Manuel d'utilisateur télécharger pdf (Page 24)

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f is not continuous at a if there is an  > 0 such that for all δ > 0

there is an x satisfying |x − a| < δ such that |f(x) − f (a)| ≥ ,

which I think is the right answer!

Conclusion

The key to this use of ﬁrst order logic seems to be, if C(x) is the condition

on x and I(x) is the implication of x satisfying the conditions, then write

the universal formula

U = ∀x(C(x) ⇒ I(x))

if the implication is true, and the existential formula

E = ∃x(C(x) ∧¬I(x))

if the implication is false. Then U = ¬E, as required, and C(x) always

appears in a positive sense to limit the bound variable to its correct domain.

In the Hilbert Hotel laundrette

Martin Cooke

In the Hilbert Hotel laundrette

They can’t keep coloureds separate:

They try to divide all the Reds

From all the not-Reds, in their heads,

By slicing lines through the rainbow

Between which all Red things would go,

But whilst these lines’ sides are then tinged

Indistinctly, they’d be unhinged

If they thence take, as Red, yellows

Pinks and their spectral bedfellows,

Or if they too readily let

Elusively captioned scarlet

Evict crimson. Naturally

Wholesome numbers like 1,2,3, . . .

Aren’t totally collectable,

Even on an endless table:

If they reach something inﬁnite

Then that’s one more than some ﬁnite,

But if they always stay ﬁnite

They’ll never have reached each ﬁnite . . .

So this Hotel is a building

That they must always be building;

Not because it’s time-and-spatial,

But, like N, since it’s sequential.

1 2 ... 19 20 21 22 23 24 25 26 27 28 29 30 31 32

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Motorola M500 Manuel d'utilisateur Page 24