Math action like drill and practice help a kid increasing great mental number aptitudes. In addition, if the training is done regularly through playing around, youngsters effectively get acquainted with numbers.
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Ok, it's time for a #FUNctionalAnalysis thread! Let's talk about Hilbert spaces. (I hope you like linear algebra, because that's what we're
If you want to impress people, you can just say a Hilbert space is just a complete infinite dimensional inner product space and leave it at that, but let's talk about what that actually means.
When you first learn about vectors, you talk about them as arrows in space; things with a magnitude and a direction. These are elements of R^n where n is the number of dimensions of the space you care about.
You also talk about the dot product (or inner product) as a way to tell when vectors are orthogonal. (I'm purposely saying "orthogonal" instead of "perpendicular" here, but when you actually think about arrows, it's the same thing.)
As my linear algebra students are about to see, R^n is far from the only interesting vector space. A classic example is the space of polynomials of dimension less than or equal to n
— syzygay (@syzygay1) August 9, 2020
If you want to impress people, you can just say a Hilbert space is just a complete infinite dimensional inner product space and leave it at that, but let's talk about what that actually means.
When you first learn about vectors, you talk about them as arrows in space; things with a magnitude and a direction. These are elements of R^n where n is the number of dimensions of the space you care about.
You also talk about the dot product (or inner product) as a way to tell when vectors are orthogonal. (I'm purposely saying "orthogonal" instead of "perpendicular" here, but when you actually think about arrows, it's the same thing.)
As my linear algebra students are about to see, R^n is far from the only interesting vector space. A classic example is the space of polynomials of dimension less than or equal to n
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Trump is gonna let the Mueller investigation end all on it's own. It's obvious. All the hysteria of the past 2 weeks about his supposed impending firing of Mueller was a distraction. He was never going to fire Mueller and he's not going to
Mueller's officially end his investigation all on his own and he's gonna say he found no evidence of Trump campaign/Russian collusion during the 2016 election.
Democrats & DNC Media are going to LITERALLY have nothing coherent to say in response to that.
Mueller's team was 100% partisan.
That's why it's brilliant. NOBODY will be able to claim this team of partisan Democrats didn't go the EXTRA 20 MILES looking for ANY evidence they could find of Trump campaign/Russian collusion during the 2016 election
They looked high.
They looked low.
They looked underneath every rock, behind every tree, into every bush.
And they found...NOTHING.
Those saying Mueller will file obstruction charges against Trump: laughable.
What documents did Trump tell the Mueller team it couldn't have? What witnesses were withheld and never interviewed?
THERE WEREN'T ANY.
Mueller got full 100% cooperation as the record will show.
BREAKING: President Donald Trump has submitted his answers to questions from special counsel Robert Mueller
— Ryan Saavedra (@RealSaavedra) November 20, 2018
Mueller's officially end his investigation all on his own and he's gonna say he found no evidence of Trump campaign/Russian collusion during the 2016 election.
Democrats & DNC Media are going to LITERALLY have nothing coherent to say in response to that.
Mueller's team was 100% partisan.
That's why it's brilliant. NOBODY will be able to claim this team of partisan Democrats didn't go the EXTRA 20 MILES looking for ANY evidence they could find of Trump campaign/Russian collusion during the 2016 election
They looked high.
They looked low.
They looked underneath every rock, behind every tree, into every bush.
And they found...NOTHING.
Those saying Mueller will file obstruction charges against Trump: laughable.
What documents did Trump tell the Mueller team it couldn't have? What witnesses were withheld and never interviewed?
THERE WEREN'T ANY.
Mueller got full 100% cooperation as the record will show.