Inclusion Real: A Riddle Trail

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Explore how real sets fit together

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Yhinel Santana Batista

República Dominicana

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Inclusion Real: A Riddle Trail


Inclusion Real: A Riddle TrailVersión en línea Explore how real sets fit together por Yhinel Santana Batista 1 I am a starting point for counting, yet not all of me is whole. I begin with one and can go on forever; what am I where integers are near? Hints 1 I are the building blocks for other sets like integers 2 Sometimes called counting numbers 3 I include 1, 2, 3, ... 2 I am the set of whole numbers with no fractions or decimals. Add 0, and I am still whole. What am I called? Hints 1 Commonly denoted by {0,1,2,...} 2 No fractions or decimals allowed 3 Includes 0 3 I am a step beyond counting, where negatives join the party. What set holds ..., -2, -1, 0, 1, 2, ...? Hints 1 I is denser than natural numbers 2 I include zero 3 I contain both positive and negative numbers 4 I am all fractions obtainable by dividing integers, with ration as my center. What set includes 1/2, 3/4, 5/1? Hints 1 Every element is a fraction a/b with b ≠ 0 2 Decimals may terminate or repeat 3 Made from ratios of integers 5 I am a bigger stage where decimals may never settle, yet I still contain fractions. I include irrational stars like pi and sqrt(2). What am I? Hints 1 My symbol is a horizontal line with a double stroke 2 Includes all rationals too 3 Some numbers have endless non-repeating decimals 6 I am a set that contains all real numbers but not all numbers you may imagine in geometry. What am I called, being all possible real values? Hints 1 Used to plot real-valued functions 2 Each point corresponds to a real value 3 Represents all real numbers on a line 7 I am the rule saying one thing is inside another. When A is inside B, we say what? Hints 1 Key idea in inclusions 2 Used to compare size of sets 3 A contains all elements of B? 8 Sometimes we compare how many things are in a union or separate parts. Which operation helps us count distinct items from A and B? Hints 1 Common in probability and combinatorics 2 Helps avoid double counting 3 Deals with overlaps in sets 9 I am the smallest unit distance on the real line between two distinct real numbers. What am I? Hints 1 Nonnegative by definition 2 On the line, it measures gap 3 Distance is the absolute value of difference 10 I link the real numbers to complex numbers by adding an imaginary counterpart. What inclusion am I describing? Hints 1 Defines how complex numbers extend reals 2 C contains R as a part of it 3 Every real number is a complex number with zero imaginary part

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Inclusion Real: A Riddle Trail

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Inclusion Real: A Riddle TrailVersión en línea

por Yhinel Santana Batista

I am a starting point for counting, yet not all of me is whole. I begin with one and can go on forever; what am I where integers are near?

Hints

I am the set of whole numbers with no fractions or decimals. Add 0, and I am still whole. What am I called?

Hints

I am a step beyond counting, where negatives join the party. What set holds ..., -2, -1, 0, 1, 2, ...?

Hints

I am all fractions obtainable by dividing integers, with ration as my center. What set includes 1/2, 3/4, 5/1?

Hints

I am a bigger stage where decimals may never settle, yet I still contain fractions. I include irrational stars like pi and sqrt(2). What am I?

Hints

I am a set that contains all real numbers but not all numbers you may imagine in geometry. What am I called, being all possible real values?

Hints

I am the rule saying one thing is inside another. When A is inside B, we say what?

Hints

Sometimes we compare how many things are in a union or separate parts. Which operation helps us count distinct items from A and B?

Hints

I am the smallest unit distance on the real line between two distinct real numbers. What am I?

Hints

I link the real numbers to complex numbers by adding an imaginary counterpart. What inclusion am I describing?

Hints