Recent content by Mike_bb

It needs infinitesimal microscope to see this infinitesimal number.

It's algebraic definition of hyperreal numbers. But how will it look on the hyperreal line?

Ok. How to take infinitesimal numbers on hyperreal line?

Hello! I considered number line and I couldn't take random points that correspond to hyperreal numbers on the hyperreal line. Instead it was points A, B, C that correspond to real numbers. How to take random point that corresponds to hyperreal number on the hyperreal line? Thanks.

You didn't understand me and I didn't understand you)) I mean that we can obtain point on plot if we'll consider vector or function. In our case, we use function for this purpose. For example, ##\vec a(x,2x)## we can represent as function ##y=2x## and we can see on the plot that point (1,2) and...

We can obtain point in coordinate system if we use functions (as you mentioned above) for visualise points (and surface consists of this points).

I mean that we can obtain coordinate that we need if we use functions. For example, for ##\vec a=(x,2x)## we can use ##y=2x## and we'll obtain set of points.

In 4D space with coordinate system XYZW (X,Y - real axis, Z, W - imaginary axis) we can obtain point. Is it right?

If I understand you correctly we can obtain set of points if we represent complex vector as complex function. Is it true?

Do you propose to represent complex vector as complex function?

Thanks! Good answers! :smile: I think how to visualise ##\vec a=(a_1+a_2i, a_3+a_4i)## in 4D space without using this form: ##\vec a=(a_1,a_2, a_3,a_4)## If anyone know how to visualize complex vector ##\vec a## in this way then explain me please.

Hello! 1) I read about complex vectors and I tried to imagine how it would look like in coordinate system. I was confused because complex vector consist of two vectors ##\vec a## and ##\vec b## : ##z=\vec a+ \vec bi##. I know that this complex vector can be visualized in 4D space. But I can't...

Thanks. What do you think about "the class generated by h(t)=t could be a first order infinitesimal number"? Does it mean that h(t)=t is infinitesimal function (t->0)?

Hello! I'm studying Synthetic Differential Geometry and I read about model construction of SDG. I found such source: http://www.iam.fmph.uniba.sk/amuc/_vol-73/_no_2/_giordano/giordano.pdf I have questions about extension R to *R and about definition of first order infinitesimal using...

Thanks to all!