/sci/ - Science & Math

OP here btw, I also want to learn more about the formal structure of math.
the theory of logic, proofs, formal structures, math structures, etc.

>>12383452
True and trivial

>>12383475
[math]a\mathbb{R} = \mathbb{R}, a \in \mathbb{R}[/math]
is this true then?

>>12383485
Not when a=0

>>12383515
[math]\frac{\mathbb{R}}{0}=\mathbb{J}| \mathbb{J}*0=\mathbb{R}[/math]
what about this?

[eqn]2\mathbb{Z} = \{..., -4, -2, 0, 2, 4, ...\}[/eqn]
[eqn]\mathbb{Z}^2 = \{0, 1, 4, 9, ...\}[/eqn]
[eqn]\mathbb{Z}^{1/2} = \{..., \sqrt{3}i, \sqrt{2}i, i, 0, 1, \sqrt{2}, \sqrt{3}, ...\}[/eqn]
thoughts on this?

>>12383569
>thoughts on this?
You merely gave suggestive names to some sets.
Any arithmetic operations leave the set.

>>12383579
yeah but I can't map the third one over R.

[eqn]\mathbb{R}^2=\mathbb{R}[/eqn]
how about this one?

>>12383634
i meant
[eqn]\mathbb{R}^2=\mathbb{R}^+[/eqn]

>>12383452
Multiply ever R number by every irrational number.

There are more irrational numbers suddenly, than rational.

>>12383452
Which is why you algebra of infinity's is meaningless

>>12383639
>>12383634
yes that's still equal

2^R > R
it doesn't get bigger until you start doing powers

>>12383452
>half it's size
>half it is size

>>12384597
what do you think about pic related?
>>12384806
When I type it's entirely muscles memory. I'm used to using apostrophe s for possessive objects, so it just happened automatically.
*its

Scientifically speaking why am I in love with Hitomi?
I've began going on a diet and working out for her.
I think my mom thinks I have a girl friend.

>>12383464
read about Dedekind cuts

I don’t really know why someone would care about set equality this way.
What you said is true, it’s just not particularly interesting.
If you consider something where this isn’t true, like the integers, it doesn’t really matter still because they still have the same cardinality, they still have the same structure as additive groups, etc. so all you’ve done is just relabel things nicely
Isomorphism in a specific context is just much more worth considering most of the time

>>12385003
I think it's pretty interesting especially when thinking about the numbers in the neighborhood of infinity.

>>12383532
>reals multiplied by the nonexistent multiplicative inverse of 0
sigh

>>12385156
it works for R*i.
you're right the J set isn't real, DUH.

Algebraically speaking what is square rooting?
or generally taking the root of something.
what arithmetic process or algorithm represents that?
I mean taking the power of something can be described very easily.

>>12386323
it's one of two inverses of exponentiation (the other being logarithm)

>>12386323
Square rooting in the reals means finding [math]x \in \mathbb{R}_+:x^2=y[/math] for some [math]y \in \mathbb{R}_+[/math]. So algebraically find that x such that [math]x\cdot x = y[/math]

>>12383452
it's clearly bullshit, just like 1+2+3...=-1/12.
The fact that such an outcome exists, and is logically defensible, proves that the logic itself is broken.

Yet mathcucks will continue to defend this, and insist R=2R due to some abstract and poorly defined nonsense.

>>12383452
>thus logically if I multiplied every number in the set R then every number there is the same as in the set 2R
Why can't anyone on this fucking board write a coherent sentence?

>>12384617
What about [math]1.5^{\mathbb{R}}[/math]

>>12383634
What about [math]1.5^{\mathbb{R}}[/math]?

>>12384617
>>12387762
Well?

>>12384617
>>12387762
>>12387784
What about [math]\lim_{x\to\infty}(1+\frac{1}{x})^{\mathbb{R}}[/math]? Is that bigger than R?

>>12387739
It's probably a combination of non-native speakers who learned English from twitter, and the tiny default text-entry window.

>>12385227
>>12383532
/sci/ - science and bullshit