Cantor showed that the "integer grid" has the exact... same number of points as the "integer line"—even though both have infinitely many points! The correspondence can be shown using two (& only two!) bijective quadratic functions sending pairs (x,y)∈ℕ₀×ℕ₀ to integers n∈ℕ₀.show more

Using a Joystick with the Feather Offset, you can... make the light change as you move the cursor. You only need to create two animations, one for the horizontal movement of the light and shadows, another for the vertical movement, and connect both to a joystick. Have fun!!show more

Many Christians choose to break the covenant of circumcision... even though the covenant should be everlasting, but at the same time, they say God will never flood the Earth again because He made a covenant and the rainbow is the sign. So why do people think they can break covenants, but God can't, even though the Bible is clear that God can withdraw judgment if there is repentance, and He can also withdraw a blessing if there is disobedience? Also, the promise might be for a certain Age or Aion. Life will not be destroyed entirely, the same as it was not destroyed during Noah's Flood. Everything points out that the Flood is a cyclical event, and being born again from water, or purification by water and baptism, is connected to the Flood.show more

JUST IN: China has reportedly deployed multiple warships to... the Middle East region after the United States deployed two carrier strike groups. Up to 6 Chinese warships were reportedly deployed including two advanced 052D destroyers. The news comes as the United States has prepared to deploy more troops to the region. The exact number is currently unknown. "I will continue to assess our force posture requirements in the region and consider deploying additional capabilities as necessary," said Secretary of Defense Lloyd Austin. It didn’t have to be this way…show more

⚽️👇 Activity Instructions This is a switch of play... rondo from This rondo is designed to develop quick and intelligent switches of play in possession. The game begins with a 3v1 in one area of the grid while two additional defenders are positioned to screen the central zone. Possession players must complete a set number of passes (e.g., 5) before attempting to switch play to the opposite side. Switches can be made in two ways - via the wide unopposed players for 1 point, or through the central zone for more points due to the difficulty and risk involved. This setup encourages decision-making, timing, and awareness of space and pressure. 🎨 Animation Created on The Tactics Appshow more

PVL ON TOUR CHANGES AND INNOVATIONS 🏐 The PVL... has announced the following rule changes and innovations for this year's PVL on Tour. 🔸 Each winning team per game will win P100,000 while the losing team will receive P50,000. 🔸 All 14 players per team must have already played by the end of Set 2, with each player required to be part of at least three rallies. 🔸 The two-point Premier Ball, similar to the one used in the All-Star Game, will again be used in the PVL on Tour. It can only be activated until a team reaches 22 points in Sets 1 to 4, and until 12 points in Set 5. #PVL2026 #PVLonTour #AlasPilipinasshow more

I’m guessing that the combo of fat positivity +... early menopause explains the FTM wheelchair phenomenon. The FTM cane 🦯 user phenomenon is best explained by psychosomatization/ being white & needing a cane for extra oppression points. I sh*t you not. I knew many trans 🏳️‍⚧️ identified young women. Around 20 of them (combined from different cities & countries) and they all required mobility aids about four, five years in. It was one or two if they were really obese & inactive The T pushed whatever issues they had way over the edge. Only two of them seemed like they were psychosomatizing because those were the two with the canes & the brightly colored trans stickers on them . Wheelchairs are way too expensive to get even if they are medically necessary, to use one as a tool to gain victim points.show more

Footage showing one of two Russian Geran-2 drone strikes... on a Ukrainian passenger train in Shostka, Sumy Oblast, from yesterday. The locomotive hit is No. ChME3 1816, and interestingly that same exact train was seen in September of this year covered in anti-drone netting. Additionally, the cargo cars can be linked back to Chornomorsk, Odesa Oblast, and that exact type has been used for maritime military purposes.show more

The bgm for this scene of holding an umbrella... in the snow is “The Return Line of Love” (爱的回归线), a song both of them have sung before! The song’s meaning is that even if people part ways, true love, like a planet, follows its orbit and can return to the same point - the “return line.” It’s a metaphor for destiny, second chances, and the belief that everything happens in its own time. One beautiful line from the lyrics goes: “There are so many people in the world, yet I met you.”show more

7/8 Two monkeys tried to challenge Shikano today. The... monkey that challenged Miyakoshi yesterday seems to be the same one. One of the older monkeys tried to warn the younger one, but the youngster even touched Shikano's shoes! In the end, they calmed down and left Shikano alone. I wonder why they're behaving like this lately. Are they being curious, playful, or trying to test boundaries? Both dads must be careful with them . If shikano and miyakoshi don't have safty how punch can be eat peaceful in during mealtime ?.🤔 #ichikawazooshow more

Situation on Aleppo, Raqqa & Hasakah [2/2/2026]: On 30... January, a definitive ceasefire was agreed following an agreement reached between the Syrian Transitional Government & the Syrian Democratic Forces for the gradual political and military integration of the SDF. Among the points agreed upon, it is worth noting the limited deployment of MOI forces on the "line of separation" between the SDF/YPG and the STG, which have withdrawn from much of the front line. There will also be a limited deployment of the MOI in the cities of Qamishli, Hasakah and Kobani, as well as at the Sweidiyeh oil wells and border posts. In exchange, the SDF will create four positions that will be incorporated into the Damascus military apparatus, both directly and indirectly, as well as decision-making powers for the SDF in the governorate of Hasakah, which could be considered a form of autonomy alongside the rights promised to the Kurds two weeks ago. During the early afternoon of today, MOI forces began their coordinated deployment with Asayish forces in Hasakah and Kobani for the time being.show more

External cues can be capped at times, especially since... there are only so many points on the field we can tell hitters to hit the ball to. So, since we know they're king 👑what's another way we can implement them? Everyone has hit two seams off of the tee before with the thought of hitting the inside seam, but we can also hit the outside seam and achieve some cool results. Watch how Marcus gets pushy and hits the ball 18 inches in front of the plate at 100 EV with topspin. When we switch focus to the outside seam, he rotates behind the ball and catches it deeper allowing him to create backspin and launch pull side at 104.5 🔥 Christian Leoneshow more

😥 Sorry for the late update on the progress... of our fishing ground development: Currently, 80% of the functions have been completed, and some values need to be adjusted repeatedly.🙏 Regarding the introduction of the fishing ground, we can reveal a few points:👇 1️⃣You can use flt to buy fish treasure chests, and after opening them, you can get different types of fish. 2️⃣There are different levels of shared fish ponds for the entire server. The higher the level of the fish pond, the more resources it produces. 3️⃣After you get the fish, you can put them in the fish pond. The fewer fish in the pond, the more resources each fish can get. Conversely, the more fish in the pond, the fewer resources are allocated to each fish. 4️⃣You need to synthesize your fish (only fish of the same species can be synthesized) in order to put them in the higher-level fish pond. At the same time, the stronger your fish, the more resources you will get. 5️⃣Of course, raising fish is not completely risk-free. When the number of fish in the pond reaches a certain level, you will be able to fish. The more fish in the pond, the higher the probability of being caught. 6️⃣You can also strengthen your fishing rod to increase your chances of catching fish.show more

Only Tribalism can save the West Ironically, it’s going... to be the same concept that destroys it As we “progress” through time you’ll see Pagans vs Christians, Christians vs Pagans But no two Pagans or Christians agree 100% with each other Even they will destroy each other Now is the time to develop your Tribe and make alliances Now is the time to prepare for the Modern Fall of Rome The only Tribes that survive will be those whose God or Gods is on their side Out of this darkness and desolation those Tribes who remain will build again And thus, a New Cycle will begin of Humanity will beginshow more

The necklace Charlie was wearing had to be sterling... silver because the Chevron cross pendant was only available in sterling and the necklace matches the pendent in color spectrum. Sterling has a lower melting point than stainless and a higher conductivity but that second point doesn't really matter because conductivity wise flesh is about 10⁸, (eight orders of magnitude, using the muscle) more resistant than sterling. The SM58 couldnt be the source of electricity. It's shell is tied to pin 1 (shield). So "shocked by an SM58" means shocked by something upstream — a mixer, amp, or power conditioner with a leakage path — delivered through the mic body. The mic is a conductor in the circuit, not the origin. Voltage isn't conducted; current flows through a path. A conductor only carries current if it bridges two points at different potential. A necklace resting on a neck touches skin along its whole length - all of it sits at essentially the same potential as that skin. It bridges nothing, so it carries essentially nothing, regardless of what it's made of.show more

Dear Ashwini Vaishnaw ji, We are so happy that... you are relaunching the IRCTC website in 30 days. Instead of working on CAPCHA, please ensure the following: 1. The Site should not crash during Tatkal bookings. Zero crashes especially during payments. 2. Ensure that Senior Citizens get Lower Berths (even now, many Senior citizens get Middle or Upper) even if they book a little later (Algorithm can be fixed) 3. Introduce More General Coaches to accommodate more Travelers 4. Strict Penalty for Unreserved Passengers occupying Reserved Seats. Work on AI cameras to detect this 5. RAC passengers should only pay half the fare for half the seat. So, once chart is prepared, please refund the 50% fare. This can easily be incorporated using simple technology. 6. If any train is delayed for more than 2 hours, refund should be issued automatically. 10% per hour delay. This can be done with some technology. 7. People's time should be valued. Tech can be used for the same. CAPCHA can wait. These things cannot !!! Request my audience to add more points so that the new website can have all these things in next 30 days 😍 #FIshow more

Please explain: The photo you shared is from the... exact same angle as the surveillance video that was submitted as evidence during the preliminary hearing. Are you suggesting that there are two videos from the exact same angle, one in higher resolution from which you got the still, and the other grainier, wide-angle surveillance footage that was submitted as evidence at the preliminary hearing? Or are you suggesting that the original video was in high resolution, and the video footage submitted as evidence during the preliminary hearing was altered/distorted before being submitted? FYI: this will not be the first time people shared an AI enhanced version of a screenshot claiming “this is not Tyler Robinson” And while I have your attention: have you released the unredacted receipt yet? The one from the steakhouse that definitively proved that Tyler Robinson was eating dinner at 10 o’clock, and could not have gotten to Orem to send the text at 11? I don’t think you released that yet, despite the promises.show more

Please explain: The photo you shared is from the... exact same angle as the surveillance video that was submitted as evidence during the preliminary hearing Candace Owens Are you suggesting that there are two videos from the exact same angle, one in higher resolution from which you got the still, and the other grainier, wide-angle surveillance footage that was submitted as evidence at the preliminary hearing? Or are you suggesting that the original video was in high resolution, and the video footage submitted as evidence during the preliminary hearing was altered/distorted before being submitted? FYI: this will not be the first time people shared an AI enhanced version of a screenshot claiming “this is not Tyler Robinson” And while I have your attention: have you released the unredacted receipt yet? The one from the steakhouse that definitively proved that Tyler Robinson was eating dinner at 10 o’clock, and could not have gotten to Orem to send the text at 11? I don’t think you released that yet, despite the promises.show more

Enerhodar. We have recorded from Nikopol that the Russian... occupiers have started a fire on the territory of the Zaporizhzhia Nuclear Power Plant. Currently, radiation levels are within norm. However, as long as the Russian terrorists maintain control over the nuclear plant, the situation is not and cannot be normal. Since the first day of its seizure, Russia has been using the Zaporizhzhia NPP only to blackmail Ukraine, all of Europe, and the world. We are waiting for the world to react, waiting for the IAEA to react. Russia must be held accountable for this. Only Ukrainian control over the Zaporizhzhia NPP can guarantee a return to normalcy and complete safety.show more