Show that the following pairs of sets S and T are equinumerous by finding a specific bijection between the sets in each pair.

S = [0,1] and T = [0,1)

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- October 20th 2009, 09:48 AMp00ndawgBijection between Sets(again)
Show that the following pairs of sets S and T are equinumerous by finding a specific bijection between the sets in each pair.

S = [0,1] and T = [0,1) - October 20th 2009, 10:05 AMaman_cc
- October 20th 2009, 10:27 AMPlato
- October 20th 2009, 10:40 AMaman_cc
Plato - Thanks.

Please validate my understanding. You have used a technique similar to the argument used in Hotel Infinity Paradox - To make room available ask every occupant to shift to the next room.

Consider F: [0,1]->[0,1]

If I remove finite points from the range - I can use your argument to construct a bijection. Correct?

Say if range is (0,1), I will map 1/n -> 1/(n+2) and 0 -> 1/2

Correct plz? - October 20th 2009, 10:44 AMp00ndawg
- October 20th 2009, 10:51 AMPlato
- October 20th 2009, 11:14 AMp00ndawg
what do you mean by when x != (1/n)?

im working on the injection on surjection right now, but when x != (1/n) is that for everything in S = [0,1] ? - October 20th 2009, 11:49 AMPlato
- October 20th 2009, 02:27 PMp00ndawg
Okay! thank you! I think im finally getting it.

I just have one more question, when im looking at these two sets how would I know to

separate it into a function like that?

is it just practice? or is there anything from that set that is setting off some alarms in your head?

thanks a bunch!