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Showing posts from July, 2013

Math: Calculus (Integral) Proof 0 ≠ 1

A fun time — in mathematics. This one sophism is using integral and it is taken from Mudd Math Fun Facts — the calculation ends up with 0 = 1 . The link is also gone now, as they revamped the website. Sophism means a fallacious argument, especially one used deliberately to deceive. Sophisticate originates from sophisticus (Medieval Latin), while sophism is from Greek sophisma — different origins, but lo! Sophism and sophisticate, both have sophis . And yes, sophism has its sophistication. Quoted Consider the following integral: ∫(1/x) dx -------------------------------------------------- Perform integration by parts: Let u = 1/x dv = dx du = -1/x² dx v = x -------------------------------------------------- Then obtain: ∫(1/x) dx = (1/x).x - ∫x(-1/x²) dx = 1 + ∫(1/x) dx ❓ Let's take a look at that last line, and continue that: The last line: ∫(1/x) dx = (1/x).x - ∫x(-1/x²) dx = 1 + ∫(...

High School Math: Proof 1 ≠ 0

First of all, of course, 1 ≠ 0 . One is not zero. If they were similar, blimey! Imagine how the bridge construction would be and how many of us would chew beams . The steps: chair ≠ banana Counterexample: Bob ate a chair yesterday. Hi, Bob. It's your board room meeting suggestion which led to the two-layer right-click menu in Windows 11, innit? 🤔 Let's dissect the proof from Mudd Math Fun Facts which yields 1 = 0 — the link is gone now. 😂 Quoted A bit paraphrased. Consider two non-zero numbers x and y such that: x = y ------------------------------------------------------------ Then x² = xy (multiplied by x) Subtract both sides with y²: x² - y² = xy - y² ------------------------------------------------------------ Divide by (x-y), we obtain: x + y = y Since x = y, we see that: 2y = y ------------------------------------------------------------ Thus 2 = 1 (divided by y), since we started with nonzero y. -----------------------------...
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