Does the intersection of a countable descending family of measurable sets of infinite measure still have infinite measure?

Let $(A_k)_{k=1}^{infty}$ be a countable family of measurable sets with $m(A_k)=infty$ and $A_{k+1}subseteq A_k$ for each k$in Bbb N$, is it necessary that $m(cap_{k=1}^{infty}A_k)=infty?$

coalgebras – This is a problem about infinite order permutation groups

That’s the problem :let A be an infinite set.let D be the subgroup of Permutation group of A which move only a finite number of elements of A and let A be the set of all elements x∈D such that acts as an even permutation on the finite set of points it moves.prove that A is an infinite simple group.
My confusion :Prompted me to prove that each pair of elements of D is in a finite simple group of D.I think this means that every element in the D is in a finite single group of D and I think the finite single group will be an alternating group.But isn’t there a odd permutation in D

magento2.3.1 – Magento checkout page goes hangs and infinite loop circle revolves after paypal payment fails

When customer is doing transaction on our website and going for payment to paypal and enters all details related to payment.
The user lands on checkout page on our magento website and circle spins continuously and transaction fails without any error message
Current Magento Version – 2.3.1
Error in logs
main.critical: paypal nvp gateway errors: the field shipping address postal code is required.

Error in Paypal logs attached,.
Please help us on this.

c# – Stop Infinite Jumping in Unity 2D

I’ve got my jump down but I cant find a way to stop infinite jumping.
Heres my code:

public class Jump: MonoBehaviour
public float speed = 5f;
public float jumpSpeed = 8f;
private float movement = 0f;
private Rigidbody2D rigidBody;

private bool isGrounded;
public Transform groundCheck;
public float checkRadius;
public LayerMask whatIsGround;

void Start()
    rigidBody = GetComponent<Rigidbody2D>();

// Update is called once per frame
void FixedUpdate()

    movement = Input.GetAxis("Horizontal");
    if (movement > 0f)
        rigidBody.velocity = new Vector2(movement * speed, rigidBody.velocity.y);
    else if (movement < 0f)
        rigidBody.velocity = new Vector2(movement * speed, rigidBody.velocity.y);
        rigidBody.velocity = new Vector2(0, rigidBody.velocity.y);
    if (Input.GetButtonDown("Jump"))
        rigidBody.velocity = new Vector2(rigidBody.velocity.x, jumpSpeed);

    isGrounded = Physics2D.OverlapCircle(groundCheck.position, checkRadius, whatIsGround  );

postgresql – System.InvalidCastException: infinite timestamp values ​​cannot be converted to DateTime

I have a strange problem that seems to be specific to my postgres database on my test server and not my local database.

Every time I insert something into my database I get an error

System.InvalidCastException: Can't convert infinite timestamp values to DateTime

And I can't seem to understand why I'm getting this error on a remote server and can't replicate it locally?

from a google search seems to be fixable by adding Convert Infinity DateTime to truth

but this doesn't seem to work?

But again, does it seem to be specific to the environment in which it runs? Can this affect you in any way? Maybe something like a version that doesn't work or something else?

I can't seem to understand why it works in one database but not another.

I should be using the latest version of postgresql-12, but somehow I can verify this.

Exception":"System.InvalidCastException: Can't convert infinite timestamp values to DateTimen   at Npgsql.NpgsqlDataReader.GetValue(Int32 ordinal)n   

Complex variables from to show the holomorficity of a certain infinite series of functions

Yes $ Re (s)> 1/2 + epsilon $ for $ epsilon> 0 $ we have $ log (1 + p ^ {- s}) = sum_ {j = 1} ^ infty p ^ {- sj} / j $ so
$ | f_p (s) | le sum_ {j = 2} ^ infty p ^ {- Re (s) j} / j le p ^ {- 1-2 epsilon} / (1-p ^ {- 1 / 2- epsilon}) $. As $ sum_p p ^ {- 1-2 epsilon} $ converges, its series converges uniformly in $ {s: Re (s)> 1/2 + epsilon } $, and therefore the sum is holomorphic there, and in particular this is true in $ R $.

real analysis – infinite series convergence

$ (c_k) $ it is a sequence of real numbers. It's known that $ lim_ {x a 1 ^ -} c_k y ^ k $ There is also $ lim_ {k to infty} kc_k = 0 $ and $ sum_ {n = 1} ^ { infty} c_ky ^ k exists for all and in (0,1) $. And suppose for every $ y in (0,1) $ we take G (y), which is a natural number and depends on x, so that $ G (y) leq frac {1} {1-y} leq 1 + G (y) $. I want to prove that $ lim_ {y a 1 ^ -} sum_ {k = 1} ^ {G (y)} c_k (1-y ^ k) = 0 $ and
$ lim_ {y a 1 ^ -} sum_ {k = 1} ^ {G (x)} c_k $So finally I want to show that $ lim_ {y to 1 ^ -} sum_ {k = 1} ^ {G (x)} c_k = lim_ {y to1 ^ -} sum_ {k = 1} ^ { infty} c_ky ^ k $.
I tried the following:
by $ 0 leq x <1 $, sequence $ (y_n) $ it is monotonically decreasing and limited, and therefore the Abel test can be used. So, $ sum_ {n = 1} ^ { infty} c_ {2n} and ^ {2n} $ and $ sum_ {n = 1} ^ { infty} c_ {2n-1} and ^ {2n-1} $ are convergence due to $ sum_ {n = 1} ^ { infty} c_ {n} y ^ {n} = sum_ {n = 1} ^ { infty} c_ {2n} y ^ {2n} + sum_ {n = 1} ^ { infty} c_ {2n-1} and ^ {2n-1} $. But then I feel that something is wrong.
I'm confused. I want to do it using elemental analysis. Please help!

Any automated infinite scroll news script?

Imagine, you provide some keywords and the script shows short news in infinite scroll.

If possible, comply with copyright by using news from other sites

thanks in advance

Infinite World Floor Grid Shader

I am trying to render an infinite world floor grid as seen in most 3D modeling tools, similar to this question. The project is using the metal shading language, but the concepts are certainly similar between GLSL / HLSL.

Here is a sample project that shows the current status of an attempt to render a plane as a full-screen quad with the grid lines drawn in a fragment shader.

In order for the ball to roll, I first set up a quad on the xy plane with a width and height of 10 and render it with a standard program to set the position and coordinate of the grid:

//inside floor_vertex()
f.position = scn_node.modelViewProjectionTransform * float4(v.position, 1.0);
f.coordinate = v.position.xy;

The fragment shader determines what color to render the grid or floor:

fragment half4 floor_fragment(FragmentIn f ((stage_in))) {

    float2 position = f.gridPosition;
    float2 fractional  = abs(fract(position - 0.5) - 0.5);
    float2 partial = fwidth(position);

    float2 g = smoothstep(-partial, partial, fractional);

    float grid = 1.0 - saturate(g.x * g.y);

    return half4(mix(gridColor.rgb, floorColor.rgb, grid), 1.0);

This provides the following results (a cube is added to help visualize the rotation).

Floor shader applied to xy aligned quad

Then I remove any projection transformation and just set the vertex position as it is in the clip space to fill the screen (note: the width and height of the quadrant are set to 1 so this doesn't really fill the screen here as I was trying to debug and understand the problem even more.)

//inside floor_vertex()
f.position = float4(v.position, 1.0);
f.coordinate = v.position.xy;

Floor shader without view projection transformations

So far so good! But the grid is still aligned along the xy y-axis does not translate / rotate correctly relative to camera. This is where I am struggling to find the right shader settings. The closest I have come is transforming the coordinate with the reverse model view projection transformation, but this does not produce the correct results.

//inside floor_vertex()
f.position = float4(v.position, 1.0);
f.coordinate = (scn_node.inverseModelViewProjectionTransform * float4(v.position, 1.0)).xy;

Floor shader that responds to camera rotation

As you can see, the grid is not parallel to the cube. I realize that this is a very naive stab in a shader, as it doesn't give the impression of a grid stretching towards the horizon, especially with the disjunction between the grid transformations and other objects on the scene.

I've been using this article as a reference, but my limited knowledge of shaders and matrix transformations is certainly causing me some confusion.

Am I even on the right track? I feel like I'm making huge strides but without anyone being able to brainstorm, this feels like a drain of time that should be spent doing other things (like reading about shaders)!

Markov chain in an infinite binary tree

Consider an infinite binary tree in which its vertices can be represented as finite strings of 0 and 1. Let $ emptyset $ denotes the top vertex, also known as the "root" of the tree. Leave $ 0 <p < frac {1} {2} $ and define the transition probability as follows:

At each vertex, it has probability $ p $ to move to one of its two child vertices, and the probability $ 1-2p $ to move to its parent vertex. As $ emptyset $ he has no father we leave $ p ( emptyset, emptyset) = 1-2p $.

For what values ​​of $ p $ Is this string recurring, recurring positive, or recurring null?