<P> The first of these results is apparent by considering, for instance, the tangent function, which provides a one - to - one correspondence between the interval (− π / 2, π / 2) and R (see also Hilbert's paradox of the Grand Hotel). The second result was proved by Cantor in 1878, but only became intuitively apparent in 1890, when Giuseppe Peano introduced the space - filling curves, curved lines that twist and turn enough to fill the whole of any square, or cube, or hypercube, or finite - dimensional space . These curves can be used to define a one - to - one correspondence between the points in the side of a square and those in the square . </P> <P> Infinite - dimensional spaces are widely used in geometry and topology, particularly as classifying spaces, such as Eilenberg − MacLane spaces . Common examples are the infinite - dimensional complex projective space K (Z, 2) and the infinite - dimensional real projective space K (Z / 2Z, 1). </P> <P> The structure of a fractal object is reiterated in its magnifications . Fractals can be magnified indefinitely without losing their structure and becoming "smooth"; they have infinite perimeters--some with infinite, and others with finite surface areas . One such fractal curve with an infinite perimeter and finite surface area is the Koch snowflake . </P> <P> Leopold Kronecker was skeptical of the notion of infinity and how his fellow mathematicians were using it in the 1870s and 1880s . This skepticism was developed in the philosophy of mathematics called finitism, an extreme form of mathematical philosophy in the general philosophical and mathematical schools of constructivism and intuitionism . </P>

Where did the concept of infinity come from