For example the field of real numbers forms a structure R whose elements are the real numbers, with signature consisting of the individual constant 0 to name the number zero, a 1-ary function symbol - for minus, and two 2-ary function symbols + and . for plus and times. At first sight we can't add a symbol to express 1/x, since all the named functions have to be defined on the whole domain of the structure, and there is no such real number as 1/0. But on second thoughts this is not a serious problem; any competent mathematician puts the condition ‘x is not zero’ before dividing by x, and so it never matters what the value of 1/0 is, and we can harmlessly take it to be 42. But most model theorists are uncomfortable with any kind of division by zero, so they stick with plus, times and minus.
Schlagwort: Mathematik
42.
Mathfail.
All this fussing and primping about which “topics” should be taught in what order, or the use of this notation instead of that notation, or which make and model of calculator to use, for god’s sake — it’s like rearranging the deck chairs on the Titanic! Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion — not because it makes no sense to you, but because you gave it sense and you still don’t understand what your creation is up to; to have a breakthrough idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it. Remove this from mathematics and you can have all the conferences you like; it won’t matter. Operate all you want, doctors: your patient is already dead.
Komm utativ.
Ich packe meinen Koffer und ich packe ein
Ein Ideal, 'nen Vektorraum.
frei nach Großstadtgeflüster - Komm Schon
Singularität.
Mathematik hat den Vorteil, dass sich der Verstand auf nichts anderes konzentrieren kann.
And it's gone.
Loosing my religion seems to be the perfect song (title) for the end of your math studies.