what are hyper real numbers?

Answer 1

Hi there!

I've heard the name "hyper real" before, but I don't know much about them. I had a look on the net though, and came up with this link, which looks quite in depth and reliable: http://mathforum.org/dr.math/faq/analysis_hyperreals.html#construction

Also try having a look on wikipedia, the link is below.

From what I can make out from having a quick read of these webpages is that hyperreal numbers include infinite numbers and infinitesimal numbers (i.e. numbers that are smaller than all positive real numbers and greater than all negative real numbers, and it is possible to have non-zero infinitesimal numbers).

It helps to understand a little of real analysis, where you have what's known as an epsilon delta definition of the limit of a function, i.e. the real number R is the limit of f (a function from the real numbers to the real numbers) at a if given epsilon greater than zero there exists a delta greater than zero such that if
0<|x-a|
However, according to Wikipedia, Abraham Robinson gave a rigorous definition of infinitely large and infinitely small numbers, in what's known as non-standard analysis, and this is where the hyperreal numbers come in.

Hope this is helpful for you!

Answer 2

Never heard of them.

Maybe Dr Math has something to say:
http://mathforum.org/dr.math/faq/analysis_hyperreals.html