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Description
There are infinitely many COUNTING NUMBERS and infinitely many FRACTIONS. Which infinity is greater?

The symbol, , has been around for more than two thousand years. The Romans used it to represent 1000, a BIG number to them.

About 1650 the English mathematician, John Wallis, proposed that stand for INFINITY, and that stuck.

The concept of infinity has tantalized and sometimes troubled mankind even longer. Zeno of Elea (495 BC?-425 BC?), an early Greek thinker, is remembered for his paradoxes of motion that are rooted in deep questions about the nature of time and space and in some misconceptions about infinity. Most religions attempt to explain in their own ways the mysteries and vagaries of the infinite.

In the early 1600's Galileo began to show signs of a modern attitude toward the infinite, when he proposed that "infinity should obey a different arithmetic than finite numbers." But it was not until the late 19th century that Georg Cantor (1845-1918), a German mathematician, finally put infinity on a firm logical foundation and described a way to do arithmetic with infinite quantities useful to mathematics. His basic definition was simple: a collection is infinite, if some of its parts are as big as the whole. For example, even though from one point of view the entire list of numbers we count with {1,2,3,4,5,.......} is twice as large as the list of even numbers {2,4,6,8,10,.......}, the two lists can be matched-up in a one-to-one fashion.

Goncalo Borges Dias Photography 2006

Description
There are infinitely many COUNTING NUMBERS and infinitely many FRACTIONS. Which infinity is greater?

The symbol, , has been around for more than two thousand years. The Romans used it to represent 1000, a BIG number to them.

About 1650 the English mathematician, John Wallis, proposed that stand for INFINITY, and that stuck.

The concept of infinity has tantalized and sometimes troubled mankind even longer. Zeno of Elea (495 BC?-425 BC?), an early Greek thinker, is remembered for his paradoxes of motion that are rooted in deep questions about the nature of time and space and in some misconceptions about infinity. Most religions attempt to explain in their own ways the mysteries and vagaries of the infinite.

In the early 1600's Galileo began to show signs of a modern attitude toward the infinite, when he proposed that "infinity should obey a different arithmetic than finite numbers." But it was not until the late 19th century that Georg Cantor (1845-1918), a German mathematician, finally put infinity on a firm logical foundation and described a way to do arithmetic with infinite quantities useful to mathematics. His basic definition was simple: a collection is infinite, if some of its parts are as big as the whole. For example, even though from one point of view the entire list of numbers we count with {1,2,3,4,5,.......} is twice as large as the list of even numbers {2,4,6,8,10,.......}, the two lists can be matched-up in a one-to-one fashion.

Goncalo Borges Dias Photography 2006