PRODUCE X 101

The translation of the tweet is: "0x8c29d09b20369a0c0e4d90a2572a9243d5da4444 It's about to explode... I've been shouting about it all day..."

#NumberTheory Personally, I think the approach of demonstrating lim sin x/x = 1 through the area of a sector, as found in the current high school mathematics III textbooks, is an old method from Cauchy over 200 years ago, and it might be time to retire it. It would be better to change the approach to starting from displaying the length of a unit circle arc using the integral of the speed of (x(t), y(t)) = (√(1-t²), t).

The tweet translates to: "Since f is monotonically increasing in the broad sense for ym_n ≦ (c^n)x, we have f((c^n)x) ≧ f(ym_n). Since f((c^n)x) = c^n f(x) ≧ f(ym_n) ≧ m_n f(y), it follows that f(x) ≧ (m_n/c^n) f(y). The definition of m_n is given by (c^n)x/y - 1 < m_n ≦ (c^n)x/y, which implies x/y - 1/c^n < m_n/c^n < x/y. Therefore, by the squeeze theorem, lim[n→∞] m_n/c^n = x/y."

The translation of the Japanese tweet text to English is: "Let k = lim(x→∞) f(x)/x ∈ [0,∞]. From f(cx) = cf(x), we have ∀n ∈ Z, f(c^nx) = c^n f(x), so f(c^nx)/(c^nx) = f(x)/x (∀x > 0, ∀n ∈ Z). As n approaches ∞, we find k = f(x)/x (∀x > 0). From this, we can conclude that k < ∞ and f(x) = kx (∀x > 0)."

Here is the translation of the Japanese tweet text to English: "[Proof] It is clear that f is monotonically non-decreasing in the broad sense. For any t > 0, for x ≥ t, we have f(x) ≥ f([x/t]t) ≥ [x/t]f(t) > (x/t - 1)f(t). Therefore, f(x)/x ≥ (1/t - 1/x)f(t). Taking the lim inf as x approaches infinity on both sides gives us lim inf (x→∞) f(x)/x ≥ f(t)/t. Since t > 0 is arbitrary, taking the lim sup as t approaches infinity shows that lim (x→∞) f(x)/x exists in the range [0, ∞]."

"I want to see the entire production of BIFAR by Da-iCE, and I also want to see the entire production of Da-iCE by BE:FIRST."

The translation of the tweet is: "It's extremely popular, this token is worth ambushing."

It seems that Kudo-san is starting to get serious, which might be tough. Their singing voice is too melodic! Wowwwww! 🙂‍↕️🫧 Although they are often recognized as a performer of Da-iCE 🎲, they are also a vocalist and an all-around entertainer 🎤. They are a multi-tasker involved in songwriting, composing, providing music, and producing. Kudo-san (respect) [link to Instagram].

The translation of the tweet is: "Extremely popular, this token is worth ambushing."

The president really trusts Da-iCE, especially Kudo-san... When I thought about producing the vocal group myself, I couldn't help but think about the journey of the juniors who were nearby and haven't been rewarded much.