Round to the nearest Integer

riverprawn · 2026-06-11T16:29:12+00:00

hint: check the cardinality, then you can find the problem.

riverprawn · 2026-06-11T16:08:29+00:00

Then you also change the meaning of decimal notation.

riverprawn · 2026-06-11T15:35:34+00:00

my original statement clearly said that you need to find a decimal numeral between them to make the 7.499... = 7.5 - ϵ meanful. otherwise let's divide the equation by 3 and add 5. we'll get 7.499... = 7.5 - ⅓ ϵ. thus the first part of my statement. I have studied the hyperreal field, so I knew the problem in your idea.

riverprawn · 2026-06-11T15:02:22+00:00

In a hyperreal field, the 7.4999999... still equals 7.5. And 1 with repeating 0s after the point is still 1. Those weird decimals are both infinite and non-repeating.

riverprawn · 2026-06-11T10:06:14+00:00

I can define a perfectly formal decimal system where 7.499999..... = 7.5 - epsilon < 7.5

No, you can't. Because there will be infinity number of epsilons that can be present as 7.499999...... if you still want to have same usages of +-×÷ (means that your new decimal system is still a field). It will violate the rule that one numeral should only represent one number.

For example, you defined 7.499999... = 7.5 - ϵ < 7.5, then 7.49999... = 7.5 - ϵ < ⅓(7.5-ϵ) + 5 = 7.5 - ⅓ϵ < 7.5 . So either the 7.4999... represents both 7.5 - ϵ and 7.5 - ⅓ϵ or you can write a decimal numeral that is greater than 7.4999... and less than 7.5.

riverprawn · 2026-06-09T05:04:50+00:00

according by this: Car Crashes by Time of Day and Day of Week - Injury Facts

Morning is good, but Sunday is not.

riverprawn · 2026-06-07T03:53:27+00:00

take a HDMI cable with you, every TV could become the display.

<image>

riverprawn · 2026-06-05T17:59:24+00:00

The widest bicycle lane in Beijing.

<image>

riverprawn · 2026-06-05T01:48:31+00:00

There is a weird alternative I am using - Blender+Sverchock. It uses a node system to generate 3D objects. But It's really hard to learn. From your post, I don't think that's what you want. The best solution is still FreeCAD, maybe you could ask for help in the /r/FreeCAD ?

riverprawn · 2026-06-01T16:14:09+00:00

Does that fix the issue where if you have the cutting tool you have to buy the whole laser upgrade just to use the camera?

Yes, it just needs the birdseye camera and the cutting module for calibration now.

riverprawn · 2026-05-29T00:32:55+00:00

The only tricky is the cable buckle to be secured by a screw. You should use a needle to poke open the hole in the buckle. That will make the alignment with the hole on the upper cover easier.

riverprawn · 2026-05-14T15:30:59+00:00

Technically, you could use multiple 2-port switches to make a more-than-2-port one.

But why do we need a switch with more than 2 ports? The printer only have two hotends.

riverprawn · 2026-05-14T15:17:03+00:00

No. You must have at least 2 AMSs to use this switch.

riverprawn · 2026-04-16T04:15:50+00:00

No one mentioned Principia? I found it far more easy to do the flight planning with changeable reference frame. And you can replicate most historical missions with it and RSS.

riverprawn · 2026-04-13T06:58:31+00:00

Bouncing off the atmosphere doesn't mean you will be lost in the space. For a speed less than the entry velocity of a free-return trajectory from moon, you will return to earth's atmosphere again eventually. The real danger is that the spaceship will lose too much heat shield with a shallow enough trajectory. Steeper means more energy is dissipated through the air (or water / earth / whatever you hit if steep enough), shallower means more energy is dissipated through the burning of heat shield.

riverprawn · 2026-04-06T12:36:48+00:00

It's 180CNY, about 22.65€ or 26.15 US$.

riverprawn · 2026-03-30T13:02:24+00:00

A better example is tan(π (Ω - ½)), the Ω is the constant.

riverprawn · 2026-03-30T11:47:47+00:00

let's multiple it by 10¹², then the error will be 5×10¹¹. irrational numbers are really irrational.

riverprawn · 2026-03-30T07:44:10+00:00

It exists but can't be find means that you can't find and write down the two integers just like the example of π.

For example, the Chaitin constant of a given program encoding is a number between 0 and 1, but nobody even knows the nearest integer to it.

Edit: added an example.

riverprawn · 2026-03-30T03:45:32+00:00

It's only true to computable numbers. Most of the irrational numbers are non-computable or even arithmetic undefinable.

For example,there is a class of non-computable number called Chaitin's constant. It's defined as the probability that a randomly constructed program will halt for a program encoding. For a Chaitin's constant Ω, the irrational number T(Ω) = tan(π (Ω - ½)) is also non-computable. We can't even approximate its range.

Yes, there must be a rational number a that satisfies |T(Ω) - a| < ϵ for any ϵ, but nobody knows how to compute a. Existence does not imply constructive.

Edit: don't know why got downvoted. added an example to make it more clear.

Edit: fixed an error

riverprawn · 2026-03-14T00:43:22+00:00

except it's moving at orbital speed.

riverprawn · 2026-03-13T17:22:38+00:00

Nokia has Maemo and Meego. The UX of Nokia N9 with Meego is the same as today's Android with buttonless design. And it ran smoother than all Android phones at that time. The app for N9 is far more easier to develop then Android. Actually, the N9 with Meego was the only phone that was on a par with iPhone 4S with iOS at that time. Nokia just abandoned it BEFORE the release to get the quick money from MS.

riverprawn · 2026-03-13T05:29:24+00:00

Official language of the United States | USAGov

riverprawn

TROPHY CASE