Infinity depends on definition. Or, it might be better|
to understand as an undefined term. In any case,
it is imposible to make infinity as a mathematical
Models simulate hyperbolic geometry perfectly, but not
Lobachevsky established hyperbolic geometry with
postulate perfectly. But he relied on his own
supposition about infinity itself.
Also he judged the geometry stands up by insight
Riemann said that we can go into any world by
choosing a certain metric. But to give metric sounds
intentional and not inevitable.
It is the most reasonable that we use projective
geometry following Klein's Erlangen Programme. Be
that as it may, we still feel something kile a
We have not found a necessity to get into group
According to pologists, almost everything around us
has the hyperbolic geometry.