infinitesimals

Consider a, b, c infinitesimals such that
    a+b=c
Does it then hold that
    a=b=c
?

no

only if a = b = 0

Well then if .99... equals 1, then doesn't that have to hold?

No, for the same reason that infinity does not equal infinity.
Stop trying to apply algebra naively. Infinitesimals and infinities do not work this way.

however c+b=a like a+b=c

>>5

Actually, infinitesimals and infinities do work this way.  The problem with the line of reasoning in 4 is that 0.999... < 1 in the hyperreal numbers - equality only holds in the real numbers.

>>7
The problem with this is that some people will actually believe it.

>>7
You really want to start that troll again?  Seriously.  Kill yourself now.

Infintesimals only have a defined meaning in the hyperreal number system. Go pick up a copy of Nonstandard Analysis, fag.

FYI, hyperreal numbers have nothing to do with .9999=1, which holds in every (base 10) number system.  Troll moar plz.

All number systems work together and in the same way when it comes to algebra.  You can't honestly claim otherwise.  "Oh, I see I've got these irrational numbers here.  Better not use those with the integers.  Might fuck things up."  You can add 1 and an infinitesimal; the hyperreal system merely provides the notation with which to do this.

Your attempted use of hyperreal numbers to prove a givenly-false assertion is meaningless.  As >>5 said, infinities are not equal; nor are infinitesimals.  If x=y=z, then it cannot also be true that x+y=z, for the same reason that 1+1!=1.

Stop arguing and start learning.  lrn2research