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# Secondary Magazine - Issue 19: Focus on

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Created on 15 September 2008 by ncetm_administrator
Updated on 25 September 2008 by ncetm_administrator

 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.
Wikipedia

• 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".

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.

• 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.

• 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

• 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?

free man

 Visit the Secondary Magazine Archive Browse... Issue 19

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