Why is infinitesimal considered a number in mathematics?

[highmath]

Why infinitesimal is a "number"?!

 

[I like Serena]

Why infinitesimal is a "number"?!

An infinitesimal is:

• Not an integer number.
• Not a rational number.
• Not a real number.
• It is a hyperreal number.

 

[Monoxdifly]

What is the definition of hyperreal number?

 

[I like Serena]

What is the definition of hyperreal number?

Any of the set of numbers formed by the addition of infinite numbers and infinitesimal numbers to the set of real numbers.

 

[HOI]

I am getting the impression that "highmath", "Monoxdifly", and "UYTIYTYIUI" (on a different board) are the same person. They write in the same broken English and ask the same silly questions that are answered by basic definitions. Exactly the same question, in exactly the same wording "why infinitesimal is a number" was asked on another board where I answered, "whether an infinitesimal number is a number or not depends upon your definition of number. Infinitesmals are not "numbers" in the sense of the real number system but are in the hyperreals. Now Monoxdifly comes into ask "what are hyperreals?".

 

[RLBrown]

Why infinitesimal is a "number"?!

Click Here to get a (not rigorous) feel for hyperreal numbers.

 

[Monoxdifly]

I am getting the impression that "highmath", "Monoxdifly", and "UYTIYTYIUI" (on a different board) are the same person. They write in the same broken English and ask the same silly questions that are answered by basic definitions. Exactly the same question, in exactly the same wording "why infinitesimal is a number" was asked on another board where I answered, "whether an infinitesimal number is a number or not depends upon your definition of number. Infinitesmals are not "numbers" in the sense of the real number system but are in the hyperreals. Now Monoxdifly comes into ask "what are hyperreals?".

Who are even highmath and UYTIYTYIUI (****, that's even harder to write than my normal username)? I hope Wilmer/topsquark/MarkFL can assure you that I never use any username besides "Monox D. I-Fly" or "Monoxdifly" on any forum (I often encountered those 3 either in MMF or MHF, so I guess they are quite familiar with me. Also, broken English is quite a common trait among non-native English speakers, you know.

 

[I like Serena]

Erm... Country Boy, aren't you the same person as HallsofIvy?

 

[HOI]

Yes, and I frequent a number of different boards. But I don't ask the same silly questions on all of them. In particular, if someone pointed out a mistake I wouldn't post the same thing on a different board!

 

[S.G. Janssens]

Yes, and I frequent a number of different boards. But I don't ask the same silly questions on all of them. In particular, if someone pointed out a mistake I wouldn't post the same thing on a different board!

What you say is understandable, but personally I don't mind if people ask things even when they could be perceived as silly.
Also, it can be difficult to estimate an OP's background.

Perhaps it is like reading the papers: If I don't find something worthwhile, I move to another topic.

 

[Monoxdifly]

Yes, and I frequent a number of different boards. But I don't ask the same silly questions on all of them. In particular, if someone pointed out a mistake I wouldn't post the same thing on a different board!

While I do cross-post in different forums (MMF, MIF, here, and MHF), all of them are specific questions, not what you perceived as silly. Sorry if I sound defensive, but someone accusing me of using clone accounts really offends me.

 

[MarkFL]

While I do cross-post in different forums (MMF, MIF, here, and MHF), all of them are specific questions, not what you perceived as silly. Sorry if I sound defensive, but someone accusing me of using clone accounts really offends me.

Just to set the record straight for everyone reading this thread, none of your IP addresses show up for these other accounts. I can understand this accusation making you defensive, but I wouldn't really worry about it unless a staff member comes to you and says they have good reason to think you are using multiple accounts.

For everyone else, if you think two or more accounts are being used by the same person, please PM a staff member rather than confronting a user in public. :D

 

[Monoxdifly]

Just to set the record straight for everyone reading this thread, none of your IP addresses show up for these other accounts. I can understand this accusation making you defensive, but I wouldn't really worry about it unless a staff member comes to you and says they have good reason to think you are using multiple accounts.

Oops, sorry about that. I sometimes use different computers, sometimes at work, sometimes at home, sometimes at internet cafes, sometimes at university library, but maybe I can assure you that all of my posts are from Indonesia?

 

[MarkFL]

Oops, sorry about that. I sometimes use different computers, sometimes at work, sometimes at home, sometimes at internet cafes, sometimes at university library, but maybe I can assure you that all of my posts are from Indonesia?

We certainly do not want to discourage our users from logging in here from whatever number of different devices/networks that they want. All I looked at is whether any of your IP addresses were shared by any of the other users that were cited as potentially also being your accounts. I saw zero evidence for this. If I had, I would not have posted that information publicly but I would have discussed it with you privately if it were perceived to be a problem. We hope our users will use just one account, but we've had users use multiple account in the past, and as long as they weren't using those multiple accounts for less than desirable reasons, like vote multiple times in polls, or engage in congraulatory back slapping, upvoting, etc. then we generally don't do anything about it. It's only happened a small handful of times.