So is transfinity bigger than infinity?jbriggs444 said:
rumborak said:
mathman said:
Infinity is the idea of something being limitless or endless. It is a mathematical concept that represents a quantity or value that has no end. In other words, it is something that has no boundaries or limitations.
Infinity is a concept that refers to something that has no limit, while transfinite is a specific type of infinity that is larger than any finite number but smaller than the absolute infinity. Transfinite numbers were introduced in mathematics to help understand the concept of infinity.
Transfinite numbers are used in mathematics to represent infinite sets or quantities that are larger than any finite number but smaller than the absolute infinity. They are also used in the study of infinite series, limits, and other mathematical concepts that involve infinity.
Transfinite numbers are primarily used in abstract mathematical concepts and do not have direct applications in real-life situations. However, they provide a useful tool for understanding and studying the concept of infinity, which has implications in various fields such as physics, cosmology, and philosophy.
Cantor's diagonal argument is a proof that there are infinite sets that cannot be put into one-to-one correspondence with the natural numbers. This concept is closely related to transfinite numbers as it helped Cantor develop the theory of transfinite numbers and understand the concept of infinity in a more precise way.