Something About Infinity in Mathematics
Infinity symbolThe infinity symbol (sometimes called the lemniscate) is a mathematical symbol representing the concept of infinity. The symbol is encoded in Unicode at U+221E ∞ infinity (HTML:
∞) and in LaTeX as
It was introduced in 1655 by John Wallis, and, since its introduction, has also been used outside mathematics in modern mysticism and literary symbology.
CalculusLeibniz, one of the co-inventors of infinitesimal calculus, speculated widely about infinite numbers and their use in mathematics. To Leibniz, both infinitesimals and infinite quantities were ideal entities, not of the same nature as appreciable quantities, but enjoying the same properties.
Real analysisIn real analysis, the symbol , called "infinity", denotes an unbounded limit. means that x grows without bound, and means the value of x is decreasing without bound. If f(t) ≥ 0 for every t, then
- means that f(t) does not bound a finite area from to
- means that the area under f(t) is infinite.
- means that the total area under f(t) is finite, and equals
- means that the sum of the infinite series converges to some real value .
- means that the sum of the infinite series diverges in the specific sense that the partial sums grow without bound.