- #36
jaketodd
Gold Member
- 508
- 21
Is 2x5 the same as 2x10? Infinity can be defined, so no.TeethWhitener said:Ok so then either ##2\times\infty## is infinity or it is a finite real number. So @jbriggs444 ‘s point is still valid.
Is 2x5 the same as 2x10? Infinity can be defined, so no.TeethWhitener said:Ok so then either ##2\times\infty## is infinity or it is a finite real number. So @jbriggs444 ‘s point is still valid.
But can it be defined with the properties that you wish?jaketodd said:Is 2x5 the same as 2x10? Infinity can be defined, so no
You are correct. There are alternative number systems with definitions of ##\infty## that have been studied very thoroughly. They may not be as simple as you indicated in your original post, but they are very interesting in certain applications.jaketodd said:I think we need to study the alternative number systems more. I just know that infinity is defined in both I mention, instead of being undefined and just an idea. You say "finite real number." Both of the alternative number systems I mention are different than the real number system, as mentioned in those two Wikipedia articles. Related, but different.
This is a non sequitur. ##2\times5\neq2\times10## regardless of whether infinity is defined.jaketodd said:Is 2x5 the same as 2x10? Infinity can be defined, so no.
I think you need to study these systems more; they have already been studied extensively by mathematicians and their properties and limitations are well known as you should be able to see from the depth and consistency of the replies in this thread.jaketodd said:I think we need to study the alternative number systems more.
And on this note, time to close the thread. Thanks to all that have participated.pbuk said:I think you need to study these systems more; they have already been studied extensively by mathematicians and their properties and limitations are well known as you should be able to see from the depth and consistency of the replies in this thread.