The universe's spatial geometry, which can be flat, negatively curved (open), or positively curved (closed), dictates whether its size is finite or infinite. A positively curved universe is finite; a ...

With a surprising new proof, two young mathematicians have found a bridge across the finite-infinite divide, helping at the same time to map this strange boundary. The boundary does not pass between ...

In the past, it was generally agreed upon that the Universe was either infinite in size and age, or that it was of finite size – with the dimension of time not coming about until the birth of the ...

It was Jan. 30, 1968, the eve of the Lunar New Year. In Vietnam, this holiday is known as Tet, and tradition on Tet calls for a ceasefire in time of war. However, that tradition served as the cover ...

All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in general, research mathematicians don’t need to think about it ...

13.8 billion years ago, what we know as our Universe began with the hot Big Bang. It's been expanding and cooling ever since, up through and including the present day. From our point-of-view, we can ...

While the concept of infinity may seem mysterious, mathematicians have developed processes to reason the strange properties of infinity. Mathematician Emily Riehl has been challenged to explain ...

Receive emails about upcoming NOVA programs and related content, as well as featured reporting about current events through a science lens. Reviel Netz: Something which is equal to some of its parts.

1.Sets: Sets and their representations. Empty set, Finite & Infinite sets, Equal sets, Subsets, Subsets of the set of real numbers especially intervals (with notations). Universal set. Venn diagrams.

Of all the endless questions children and mathematicians have asked about infinity, one of the biggest has to do with its size. Whether it’s on the playground or at bedtime, children encounter the ...