a REAL cool group theory problem #shorts #grouptheory #math

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[kkanden]

remember although math is very important, your health is even more important! take care!

[aleksandervadla]

You can also argue that (R, *) has the supgroup {-1, 1}, but (R, +) has noe subgroup of 2 elements

[frentz]

they can't be isomorphic because only one of the groups has an element of order 2 (in the multiplicative group, -1 has order 2, ie -1 * -1 = 1 = the identity; the additive group has no such element)

[memesThatDank]

i love you man.
and also can't forget to thank your team!

[JM-usfr]

However, R _is_ isomorphic to R^+, the set of _positive_ real numbers. The function ln is a good example of one such isomorphism.

[mingmiao]

Thanks for the video. Take good care of your voice

[albertogarcia]

In fact any non-trivial subgroup of (R, +) is infinite (cause contains the infinite subgroup generated by a non-zero element) but the (R*, .) group has a (unique) finite non-trivial subgroup with 2 elementos {1, -1}

[xraygamer]

There was a classic problem in ring theory that is similar to this one, that asked you to show that there is no domain whose additive subgroup is isomorphic to the group of its invertible elements.

[quantspazar]

This proof only works for the reals, but the property is actually true for all fields.

[speakingsarcasm]

In general, show that the additive group of a field is not isomorphic to its group of units.

[cHAOs]

What about the equality between additive and multiplicative groups of "fi", "fo", and "fum"? Are any of these followed by hyperosmia in relation to englishmen hemoglobin as has been asserted at least once by the giants in this field?

[anshumanagrawal]

What about multiplicative group of positive real numbers? Does that have an isomorphism

[flavrt]

surjective: This vid used more obscure phrases than any I have ever seen. At once humbling and an obfuscation giggle.

[jak]

A question, why not real number is a contradiction? Why does't we just did't call it really inreal number?

[srijseekssunflowers__]

Can't we say that they aren't isomorphic because identities go to different places, 0 and 1

[TheFireBrozTFB]

Someday, i’ll understand what you mean

[SageCog-zlue]

So the proof for the Birch, Swinnerton & Dyer conjecture from y ^ 2 = x ^ 3 - x looms then?

[danielmilyutin]

I didn't get it first. And thought, what about exponent?

[shaimaasoltan]

Thank you, but if phi(x/2+x/2)=phi(x), is this means the existing of an assumption in this process, that x can be divided equally by 2 and the result still exactly equal -1. If so, why not say that phi(x/2)=-1/2.

[jakobr_]

So what you’re saying is that we might get isomorphism in C?