Tag: integers

New Cur 17: Natural Selection

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December 28, 2022

6:17 pm

11 Comments on New Cur 17: Natural Selection

New Cur

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A few weeks ago, we posted on a klutzy index law elaboration in the new curriculum:

using examples such as \color{OliveGreen}\boldsymbol{\frac{3^4}{3^4} =1}, and \color{OliveGreen}\boldsymbol{{3^{4-4}}=3^0} to illustrate the necessity that for any non-zero natural number 𝑛, \color{OliveGreen}\boldsymbol{{n^0}=1} (new AC9M8N02)

Some commenters were understandably puzzled by a side point: ACARA’s employment of the expression “non-zero natural number”. In this post, we’ll dispel any lingering lack of puzzlement.

Continue reading “New Cur 17: Natural Selection” →

WitCH 4

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September 13, 2018

11:05 am

15 Comments on WitCH 4

WitCH

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Well, WitCH 2, WitCH 3 and Tweel’s Mathematical Puzzle are still there to ponder. A reminder, it’s up to you, Dear Readers, to identify the crap. There’s so much crap, however, and so little time. So, it’s onwards and downwards we go.

Our new WitCH, courtesy of New Century Mathematics, Year 10 (2014), is inspired by the Evil Mathologer‘s latest video. The video and the accompanying articles took the Evil Mathologer (and his evil sidekick) hundreds of hours to complete. By comparison, one can ponder how many minutes were spent on the following diagram:

OK, Dear Readers, time to get to work. Grab yourself a coffee and see if you can itemise all that is wrong with the above.

Update

Well done, craphunters. Here’s a summary, with a couple craps not raised in the comments below:

  • In the ratio a/b, the nature of a and b is left unspecified.
  • The disconnected bubbles within the diagram misleadingly suggest the existence of other, unspecified real numbers.
  • The rational bubbles overlap, since any integer can also be represented as a terminating decimal and as a recurring decimal. For example, 1 = 1.0 = 0.999… (See here and here and here for semi-standard definitions.) Similarly, any terminating decimal can also be represented as a recurring decimal.
  • A percentage need not be terminating, or even rational. For example, Ď€% is a perfectly fine percentage.
  • Whatever “surd” means, the listed examples suggest way too restrictive a definition. Even if surd is intended to refer to “all rooty things”, this will not include all algebraic numbers, which is what is required here.
  • The expression “have no pattern and are non-recurring” is largely meaningless. To the extent it is meaningful it should be attached to all irrational numbers, not just transcendentals.
  • The decimal examples of transcendentals are meaningless.