Proving 1-1 Correspondence of I and J Sets

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To prove that sets I and J are in 1-1 correspondence, the discussion suggests applying the Schroeder-Bernstein Theorem. Set I consists of all real numbers between 0 and 1, while set J includes real numbers from 0 to 2. The theorem can be used to establish a bijection between the two sets by demonstrating that each set can be injected into the other. Participants express appreciation for the mathematical depth of the topic, contrasting it with simpler concepts of infinite sets. The conversation emphasizes the importance of understanding set theory in advanced mathematics.
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I have to show that for the sets:

I = \left\{ x \; | \;0 \leq x \leq 1, x \; \epsilon \; \mathbb{R} \right\}
J = \left\{ x \; | \; 0 \leq x \leq 2, x \; \epsilon \; \mathbb{R} \right\}

That I and J are in 1 - 1 correspondence. I don't want to know how to prove this but a hint in the right direction would be really useful if possible.
 
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Apply Schroeder Bernstein Theorem...

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TenaliRaman said:
Apply Schroeder Bernstein Theorem...

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Wow thanks!

Some serious maths rather than the kiddy version of infinite sets we have been learning lol.
 
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