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Secondary Magazine - Issue 19: Focus on

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 15 September 2008 by ncetm_administrator
Updated on 25 September 2008 by ncetm_administrator

Secondary Magazine  
Welcome to issue 19 of the NCETM Secondary Magazine. Fortnightly features include: The Interview, Around the regions, An idea for the classroom, 5 things to do, The Diary and Focus on. This issue, we focus on infinity.

Focus on... infinity

  • Infinity (symbolically represented with ∞) comes from the Latin infinitas or "unboundedness." It refers to several distinct concepts (usually linked to the idea of "without end") which arise in philosophy, mathematics, and theology.
  • The Isha Upanishad of the Yajurveda (c. 4th to 3rd century BC) states that, "if you remove a part from infinity or add a part to infinity, still what remains is infinity".

    Pūrṇam adaḥ pūrṇam idam
    Pūrṇāt pūrṇam udacyate
    Pūrṇasya pūrṇam ādāya
    Pūrṇam evāvasiṣyate

    That is full, this is full
    From the full, the full is subtracted
    When the full is taken from the full
    The full still will remain
  • Cantor's discovery was that there is not just one infinity, but a never-ending hierarchy, each infinitely bigger than the last. It's a mind-bending thought, but the entrance to his exotic world is a surprisingly easy and familiar concept.

    Suppose you have two collections of objects. Call them collection A and collection B. How could you tell which is bigger, or if the two are the same size? Of course, you could just count all the objects in collection A, then count all the objects in collection B, and compare the two numbers. But it might be easier (and eliminate the risk of losing count), to try to match the two sets up: pair every object from A with one from B, until one or the other runs out. Sets which can be matched up are the same size, and sets which can't are different. This idea could hardly be simpler, but in Cantor's hands it yielded an extraordinary discovery: he proved that some infinite sets can never be matched with others. So immediately we have to conclude that there are different levels of infinity, with some bigger than others.

    (Plus, Issue 47) Read the rest of this article click here.
  • If your favourite number is infinity, the BBC says:
    You are mystical and complicated, a real puzzle to everyone that meets you. You are huge, but don't worry about losing a few pounds as it won't make any difference. In fact, increasing your size won't matter either, so grab a cream bun whenever you like. At times you can be infuriating and drive your friends to the brink of madness. On other occasions, they will be dumbstruck by your boundless creativity that knows no limits. Watch out though, you do have a tendency to go on a bit.

    Read about other favourite numbers click here.
  • Imagine a hotel with an infinite number of rooms. Even if the hotel is completely full and there are no vacancies, another guest can be easily accommodated...

    Listen to the BBC Radio 4 programme A Brief History
    of Infinity: Mathematics click here.
  • An infinitely long line, for instance, is surely infinitely many centimetres long. It’s also, equally surely, infinitely many miles long. But each centimetre is a great deal shorter than each mile, so does this mean that an infinitely long line is two different lengths at once?

    Read the rest of this article, Infinity is not a number – it’s a
    free man
    from Plus, click here.

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Secondary Focus - Take a tour of the portal and see what there is to bring a sense of enjoyment to your maths lessons


Visit the Secondary Magazine Archive

Browse... Issue 19
The Interview, Around the regions, An idea for the classroom, 5 things to do, The Diary, Focus on
Departmental Workshops - Structured professional development activities
Gambling with Education?
The Diary - real issues in the life of a fictional Subject Leader
An idea for the classroom
5 things to do
The Interview
Around the regions - news, views and updates from the NCETM Regional Coordinators
Explore the Secondary Forum
Contact us - share your ideas and comments 


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