Overview
Infinity in math means endlessness, limitlessness, and unboundedness. Different levels and symbols exist, which depend on how it is defined. There are many applications in science for the endlessly fascinating concept of infinity.
Endlessness
This is the most familiar concept of infinity. The number line is endless in both directions, stretching from its origin at zero, with negative numbers to the left and positive numbers to the right. A line in geometry also is endless in both directions. One of the symbols used for infinity is ∞, which looks like a figure eight turned on its side. It is often compared to the endlessness of the Mobius strip, and also is called the lemniscate.
Figure 1: The infinity symbol against infinite space.
Limitlessness
The concept of limitlessness is related to endlessness, but is not quite the same. A familiar mathematical series such as the set of odd numbers or the set of even numbers are limitless, because the series never reaches the end. In more advanced mathematics and statistics, the idea of limitlessness is used in summations and in function analysis.
Unboundedness
Unboundedness is related to endlessness and limitlessness. A geometric plane is unbounded, because it extends infinitely in all directions. The asymptotes of the normal curve never touch the horizontal axis completely, which means that the space under the normal curve is technically unbounded.
Figure 3: The asymptotes of the normal curve never touch the horizontal axis.
Applications in Science
Theoretically, the infinity represented by the infinity symbol is only the beginning of infinity. A mathematician named Cantor showed that there are more real numbers than natural numbers comparing the two sets of numbers, and designated another symbol for infinity, using the first letter of the Hebrew alphabet, or א (aleph). The natural numbers can be represented by א0, and sets that are even more infinite are designated as א1,א2, and so on, in advanced mathematics. Infinity has many applications in science, such as the infinite universe, black holes and other singularities, and infinite values used in computer programs. Chemists, physicists, and other scientists apply calculations of infinite series and limits to data from experiments.
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