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Is an asymptote an infimum-supremum?
No, an asymptote is not an infimum-supremum. An asymptote is a line that a curve approaches but never actually reaches, while an infimum is the greatest lower bound and a supremum is the least upper bound of a set. These concepts are related to the limits and bounds of a set of numbers, while an asymptote is related to the behavior of a curve as it approaches infinity. Therefore, an asymptote and an infimum-supremum are different mathematical concepts. **
How do you determine the supremum and infimum?
To determine the supremum (least upper bound) and infimum (greatest lower bound) of a set, you need to first identify all the upper bounds and lower bounds of the set, respectively. Then, you find the smallest upper bound and the largest lower bound among them. The smallest upper bound is the supremum, while the largest lower bound is the infimum. In mathematical terms, the supremum is denoted as sup(S) and the infimum is denoted as inf(S) for a set S. **
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Joico Defy Damage KBOND20 500ml DoubleStock up and save on detoxed, cleansed locks with this double pack of Defy Damage KBOND20 2 x 50ml treatment. What do you get when you combine the JOICO legacy of super-charged hair repair and the power of damage control in a single, extraordinary product? Meet Defy Damage KBOND20 Power Masque in 50ml, Joico's brand-new, bond-building treatment that doubles down on technology for 5X stronger* hair. This strength-building masque delivers transformative results in a single treatment. • 5X stronger* hair in one use • Builds & protects bonds • Rich hydration • Instantly detangles • Normalizes pH • Color safe • PETA-approved, global animal test-free *Against combing breakage on damaged hair vs. a non-conditioning shampoo. Smart Release Technology: Our one-of-a-kind liposome delivery system packs a punch by continuously releasing a trifecta of healthy-hair ingredients - Rosehip Oil, Arginine, and Keratin—to help repair, strengthen, and protect hair from the cumulative effects of daily styling. Protective Lipid: The exact kind found in healthy hair, acts as the first line of defence to help protect hair against damage. Moringa Seed Oil: Helps provide shine and softness with antioxidants, Vitamins A and E, Zinc, and Silica –ingredients that are fundamental to creating healthy, strong, damage-resistant hair. Arginine: Arginine is a naturally occurring amino acid crucial to hair’s strength. Products that include Arginine help protect hair and rebuild it from the inside out. Ingredients Aqua (Water, Eau), Butylene Glycol, Dimethicone, Sorbitol, Behenyl Alcohol, Stearyl Alcohol, Behentrimonium Chloride, Cetyl Alcohol, Glyceryl Oleate, Parfum (Fragrance), Aminopropyl Dimethicone, Isopropyl Alcohol, Phenoxyethanol, Stearyl Dihydroxypropyldimonium Oligosaccharides, Steartrimonium Chloride, Octyldodecanol, Propylene Glycol, Arginine, Cocos Nucifera (Coconut) Oil, Moringa Oleifera Seed Oil, Citric Acid, Dipropylene Glycol, Peg-6 Methyl Ether Dimethicone, C10-40 Isoalkylamidopropylethyldimonium Ethosulfate, Peg-90m, Phosphatidylcholine, Glycerin, Arginine Hcl, Laurdimonium Hydroxypropyl Hydrolyzed Keratin, Avena Sativa (Oat) Peptide, Rosa Canina Fruit Oil, Benzyl Alcohol, Benzoic Acid, Sodium Benzoate, Tocopherol, Sodium Hydroxide, Citronellol, Alpha-isomethyl Ionone139,40 £*Shipping: 0,00 £Secure redirect to the provider
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JOICO Defy Damage Protective Shampoo 300mlProtect all hair types from the ravaging effects of daily heat styling, UV exposure, and environmental pollution that lead to dry, dull, lackluster locks with Joico’s NEW Defy Damage haircare system. This damage-defying breakthrough helps protect and strengthen hair bonds for a healthy-hair transformation you can instantly see and feel. DEFY DAMAGE PROTECTIVE SHAMPOO, for bond strengthening & color longevity. A rich, luxurious lather loaded with damage-preventing ingredients gently and swiftly sloughs away dirt, impurities, and buildup without roughing up the hair cuticle or stripping vibrant color. The result is shiny, smooth, clean strands that are wonderfully resilient and healthy-looking. Free of SLS/SLES (sodium lauryl / sodium laureth) sulfates. Ingredients Water/Aqua/Eau, Sodium C14-16 Olefin Sulfonate, Cocamidopropyl Betaine, Sodium Methyl Cocoyl Taurate, Sodium Lauroamphoacetate, Lauryl Glucoside, Disodium Laureth Sulfosuccinate, Betaine, Phenoxyethanol, Sodium Lauryl Sulfoacetate, Dimethicone Propyl PG-Betaine, Arginine, Avena Sativa (Oat) Peptide, Phosphatidylcholine, Moringa Oleifera Seed Oil, Laurdimonium Hydroxypropyl Hydrolyzed Keratin, Arginine HCl, Glycol Distearate, Guar Hydroxypropyltrimonium Chloride, Isostearamide MIPA, Polyquaternium-47, Citric Acid, Polyquaternium-7, Laureth-4, PEG-120 Methyl Glucose Dioleate, Dimethicone PEG-8 Meadowfoamate, PEG-4 Laurate, Quaternium-80, Methyl Gluceth-10, Methoxy PEG/PPG-7/3 Aminopropyl Dimethicone, Tetrasodium EDTA, Glyceryl Laurate, Tocopherol, Rosa Canina Fruit Oil, Dipropylene Glycol, C10-40 Isoalkylamidopropylethyldimonium Ethosulfate, Sodium Hydroxide, Iodopropynyl Butylcarbamate, Citronellol, Fragrance/Parfum. Gorgeous Shop20,43 £*Shipping: 2,95 £Secure redirect to the provider
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JOICO Defy Damage Protective Shield 100mlProtect all hair types from the ravaging effects of daily heat styling, UV exposure, and environmental pollution that lead to dry, dull, lackluster locks with Joico’s Defy Damage haircare system. This damage-defying breakthrough helps protect and strengthen hair bonds for a healthy-hair transformation you can instantly see and feel. DEFY DAMAGE PROTECTIVE SHIELD, to guard against thermal and UV damage.A true damage defense hero against the harsh effects of daily styling and exposure to UV and environmental pollution! This protective shield helps prevent damage and guards against color fade for beautiful, vibrant, healthy-looking hair. • Makes hair 4X more resistant to breakage during heat styling• Protects against color fade• Leaves hair soft, shiny, and healthy-looking Ingredients Water/Aqua/Eau, Dimethicone, Cetearyl Alcohol, Behentrimonium Chloride, Cinnamidopropyltrimonium Chloride, C12-15 Alkyl Benzoate, Myristyl Alcohol, Cocos Nucifera (Coconut) Oil, Moringa Oleifera Seed Oil, Arginine, Avena Sativa (Oat) Peptide, Phosphatidylcholine, Rosa Canina Fruit Oil, Tocopherol, Laurdimonium Hydroxypropyl Hydrolyzed Keratin, Arginine HCl, Silicone Quaternium-16, Aminopropyl Dimethicone, Disodium EDTA, Trimethylsiloxyamodimethicone, Dipropylene Glycol, Undeceth-11, Steartrimonium Chloride, C10-40 Isoalkylamidopropylethyldimonium Ethosulfate, PEG-4 Laurate, Butyloctanol, C11-15 Pareth-7, Citric Acid, Undeceth-5, C12-16 Pareth-9, Glycerin, Trideceth-12, PEG-6 Methyl Ether Dimethicone, Aminomethyl Propanol, Isopropyl Alcohol, Phenoxyethanol, Iodopropynyl Butylcarbamate, Citronellol, Alpha-Isomethyl Ionone, Limonene, Fragrance/Parfum. Gorgeous Shop22,41 £*Shipping: 2,95 £Secure redirect to the provider
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JOICO Defy Damage Protective Masque 150mlProtect all hair types from the ravaging effects of daily heat styling, UV exposure, and environmental pollution that lead to dry, dull, lackluster locks with Joico’s NEW Defy Damage haircare system. This damage-defying breakthrough helps protect and strengthen hair bonds for a healthy-hair transformation you can instantly see and feel. This multi-tasking hair treatment will help strengthen hair bonds, provide longer-lasting colour and protect against heat styling. Hair will have a beautiful shine and softness after being treated with this powerful at-home treatment. Ingredients Water/Aqua/Eau, Butylene Glycol, Dimethicone, Sorbitol, Behenyl Alcohol, Stearyl Alcohol, Behentrimonium Chloride, Cetyl Alcohol, Glyceryl Oleate, Cocos Nucifera (Coconut) Oil, Moringa Oleifera Seed Oil, Avena Sativa (Oat) Peptide, Laurdimonium Hydroxypropyl Hydrolyzed Keratin, Arginine HCl, Rosa Canina Fruit Oil, Phosphatidylcholine, Tocopherol, Aminopropyl Dimethicone, Isopropyl Alcohol, Stearyl Dihydroxypropyldimonium Oligosaccharides, Steartrimonium Chloride, Octyldodecanol, Propylene Glycol, Arginine, Citric Acid, Dipropylene Glycol, PEG-6 Methyl Ether Dimethicone, C10-40 Isoalkylamidopropylethyldimonium Ethosulfate, PEG-90M, Glycerin, Phenoxyethanol, Sodium Hydroxide, Citronellol, Alpha-Isomethyl Ionone, Fragrance/Parfum. Gorgeous Shop22,41 £*Shipping: 2,95 £Secure redirect to the provider
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Why is the supremum defined in this way?
The supremum is defined as the least upper bound of a set because it captures the smallest value that is greater than or equal to all elements in the set. This definition ensures that the supremum exists and is unique for bounded sets, providing a precise way to describe the maximum value of a set without requiring that the maximum value itself be a member of the set. By defining the supremum as the least upper bound, we can establish a rigorous foundation for analyzing and comparing sets of real numbers. **
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What is the difference between supremum and maximum?
The supremum of a set is the least upper bound of the set, meaning it is the smallest number that is greater than or equal to every element in the set. The maximum of a set is the largest element in the set. The key difference is that a set may not have a maximum if there is no single element that is greater than or equal to every other element, while every non-empty set of real numbers has a supremum. **
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How was the supremum of the inequality determined?
The supremum of an inequality is determined by finding the smallest upper bound of the set of values that satisfy the inequality. This is done by analyzing the inequality and finding the maximum value that still satisfies the inequality. In some cases, this can be done algebraically by solving for the maximum value, while in other cases it may require using calculus or other mathematical techniques to find the supremum. Once the supremum is determined, it represents the smallest value that the set of values can approach without violating the inequality. **
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Is the supremum of the following set not 2?
The supremum of a set is the least upper bound of the set. If the set contains an element that is greater than 2, then the supremum of the set cannot be 2. However, if all the elements in the set are less than or equal to 2, then the supremum of the set could be 2. Therefore, without knowing the specific elements of the set, it is not possible to definitively say whether the supremum of the set is not 2. **
What are the supremum and infimum of this sequence?
The supremum of a sequence is the smallest real number that is greater than or equal to every term in the sequence. The infimum is the largest real number that is less than or equal to every term in the sequence. To find the supremum and infimum of a sequence, we need to find the maximum and minimum values of the sequence. If the sequence is bounded, then the supremum and infimum will be the maximum and minimum values of the sequence, respectively. If the sequence is unbounded, then the supremum and infimum may not exist. **
What is the difference between supremum and limit superior?
The supremum of a set is the least upper bound of the set, meaning it is the smallest number that is greater than or equal to all the numbers in the set. The limit superior of a sequence is the largest limit point of the sequence, meaning it is the largest number that the sequence gets arbitrarily close to as the index goes to infinity. In other words, the supremum is a property of a set, while the limit superior is a property of a sequence. **
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JOICO Defy Damage Protective Conditioner 1000mlFor Bond Strengthening and Color Longevity. Protect all hair types from the ravaging effects of daily heat styling, UV exposure, and environmental pollution that lead to dry, dull, lackluster locks with Joico’s NEW Defy Damage haircare system. This damage-defying breakthrough helps protect and strengthen hair bonds for a healthy-hair transformation you can instantly see and feel. Replenishes moisture and builds resilience without weighing hair down, leaving strands soft, shiny, and healthy- looking after each use. Stock up and save with a handy litre bottle! Ingredients Water/Aqua/Eau, Stearyl Alcohol, Behentrimonium Chloride, Cetyl Esters, Amodimethicone, Cetyl Alcohol, Fragrance/Parfum, Behenyl Alcohol, Dicetyldimonium Chloride, Helianthus Annuus (Sunflower) Seed Oil, Glycine Soja (Soybean) Oil, Panthenol, Hydrogenated Olive Oil, Olea Europaea (Olive) Fruit Oil, Avena Sativa (Oat) Peptide, Phosphatidylcholine, Laurdimonium Hydroxypropyl Hydrolyzed Keratin, Moringa Oleifera Seed Oil, Rosa Canina Fruit Oil, Butyrospermum Parkii (Shea) Butter, Olea Europaea (Olive) Oil Unsaponifiables, Arginine HCl, Hydroxypropyl Chitosan, Arginine, Quaternium-87, Stearamidopropyl Dimethylamine, Distearyldimonium Chloride, Citric Acid, Propylene Glycol, Guar Hydroxypropyltrimonium Chloride, C11-15 Pareth-7, Trideceth-12, Laureth-9, Diethylhexyl Malate, Glycerin, Isopropyl Alcohol, Tocopherol, Tetrasodium EDTA, PEG-4 Laurate, Cetrimonium Chloride, Dipropylene Glycol, C10-40 Isoalkylamidopropylethyldimonium Ethosulfate, Phenoxyethanol, Iodopropynyl Butylcarbamate, Alcohol Denat., Sodium Hydroxide, Citronellol, Alpha-Isomethyl Ionone.50,75 £*Shipping: 0,00 £Secure redirect to the provider
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Joico Defy Damage KBOND20 500ml DoubleStock up and save on detoxed, cleansed locks with this double pack of Defy Damage KBOND20 2 x 50ml treatment. What do you get when you combine the JOICO legacy of super-charged hair repair and the power of damage control in a single, extraordinary product? Meet Defy Damage KBOND20 Power Masque in 50ml, Joico's brand-new, bond-building treatment that doubles down on technology for 5X stronger* hair. This strength-building masque delivers transformative results in a single treatment. • 5X stronger* hair in one use • Builds & protects bonds • Rich hydration • Instantly detangles • Normalizes pH • Color safe • PETA-approved, global animal test-free *Against combing breakage on damaged hair vs. a non-conditioning shampoo. Smart Release Technology: Our one-of-a-kind liposome delivery system packs a punch by continuously releasing a trifecta of healthy-hair ingredients - Rosehip Oil, Arginine, and Keratin—to help repair, strengthen, and protect hair from the cumulative effects of daily styling. Protective Lipid: The exact kind found in healthy hair, acts as the first line of defence to help protect hair against damage. Moringa Seed Oil: Helps provide shine and softness with antioxidants, Vitamins A and E, Zinc, and Silica –ingredients that are fundamental to creating healthy, strong, damage-resistant hair. Arginine: Arginine is a naturally occurring amino acid crucial to hair’s strength. Products that include Arginine help protect hair and rebuild it from the inside out. Ingredients Aqua (Water, Eau), Butylene Glycol, Dimethicone, Sorbitol, Behenyl Alcohol, Stearyl Alcohol, Behentrimonium Chloride, Cetyl Alcohol, Glyceryl Oleate, Parfum (Fragrance), Aminopropyl Dimethicone, Isopropyl Alcohol, Phenoxyethanol, Stearyl Dihydroxypropyldimonium Oligosaccharides, Steartrimonium Chloride, Octyldodecanol, Propylene Glycol, Arginine, Cocos Nucifera (Coconut) Oil, Moringa Oleifera Seed Oil, Citric Acid, Dipropylene Glycol, Peg-6 Methyl Ether Dimethicone, C10-40 Isoalkylamidopropylethyldimonium Ethosulfate, Peg-90m, Phosphatidylcholine, Glycerin, Arginine Hcl, Laurdimonium Hydroxypropyl Hydrolyzed Keratin, Avena Sativa (Oat) Peptide, Rosa Canina Fruit Oil, Benzyl Alcohol, Benzoic Acid, Sodium Benzoate, Tocopherol, Sodium Hydroxide, Citronellol, Alpha-isomethyl Ionone139,40 £*Shipping: 0,00 £Secure redirect to the provider
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Is an asymptote an infimum-supremum?
No, an asymptote is not an infimum-supremum. An asymptote is a line that a curve approaches but never actually reaches, while an infimum is the greatest lower bound and a supremum is the least upper bound of a set. These concepts are related to the limits and bounds of a set of numbers, while an asymptote is related to the behavior of a curve as it approaches infinity. Therefore, an asymptote and an infimum-supremum are different mathematical concepts. **
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How do you determine the supremum and infimum?
To determine the supremum (least upper bound) and infimum (greatest lower bound) of a set, you need to first identify all the upper bounds and lower bounds of the set, respectively. Then, you find the smallest upper bound and the largest lower bound among them. The smallest upper bound is the supremum, while the largest lower bound is the infimum. In mathematical terms, the supremum is denoted as sup(S) and the infimum is denoted as inf(S) for a set S. **
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Why is the supremum defined in this way?
The supremum is defined as the least upper bound of a set because it captures the smallest value that is greater than or equal to all elements in the set. This definition ensures that the supremum exists and is unique for bounded sets, providing a precise way to describe the maximum value of a set without requiring that the maximum value itself be a member of the set. By defining the supremum as the least upper bound, we can establish a rigorous foundation for analyzing and comparing sets of real numbers. **
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What is the difference between supremum and maximum?
The supremum of a set is the least upper bound of the set, meaning it is the smallest number that is greater than or equal to every element in the set. The maximum of a set is the largest element in the set. The key difference is that a set may not have a maximum if there is no single element that is greater than or equal to every other element, while every non-empty set of real numbers has a supremum. **
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JOICO Defy Damage Protective Masque 150mlProtect all hair types from the ravaging effects of daily heat styling, UV exposure, and environmental pollution that lead to dry, dull, lackluster locks with Joico’s NEW Defy Damage haircare system. This damage-defying breakthrough helps protect and strengthen hair bonds for a healthy-hair transformation you can instantly see and feel. This multi-tasking hair treatment will help strengthen hair bonds, provide longer-lasting colour and protect against heat styling. Hair will have a beautiful shine and softness after being treated with this powerful at-home treatment. Ingredients Water/Aqua/Eau, Butylene Glycol, Dimethicone, Sorbitol, Behenyl Alcohol, Stearyl Alcohol, Behentrimonium Chloride, Cetyl Alcohol, Glyceryl Oleate, Cocos Nucifera (Coconut) Oil, Moringa Oleifera Seed Oil, Avena Sativa (Oat) Peptide, Laurdimonium Hydroxypropyl Hydrolyzed Keratin, Arginine HCl, Rosa Canina Fruit Oil, Phosphatidylcholine, Tocopherol, Aminopropyl Dimethicone, Isopropyl Alcohol, Stearyl Dihydroxypropyldimonium Oligosaccharides, Steartrimonium Chloride, Octyldodecanol, Propylene Glycol, Arginine, Citric Acid, Dipropylene Glycol, PEG-6 Methyl Ether Dimethicone, C10-40 Isoalkylamidopropylethyldimonium Ethosulfate, PEG-90M, Glycerin, Phenoxyethanol, Sodium Hydroxide, Citronellol, Alpha-Isomethyl Ionone, Fragrance/Parfum. Gorgeous Shop22,41 £*Shipping: 2,95 £Secure redirect to the provider
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Joico Defy Damage KBOND20 500mlWhat do you get when you combine the JOICO legacy of super-charged hair repair and the power of damage control in a single, extraordinary product? Meet Defy Damage KBOND20 Power Masque in 500ml, Joico's brand-new, bond-building treatment that doubles down on technology for 5X stronger* hair. This strength-building masque delivers transformative results in a single treatment. • 5X stronger* hair in one use • Builds & protects bonds • Rich hydration • Instantly detangles • Normalizes pH • Color safe • PETA-approved, global animal test-free *Against combing breakage on damaged hair vs. a non-conditioning shampoo. Smart Release Technology: Our one-of-a-kind liposome delivery system packs a punch by continuously releasing a trifecta of healthy-hair ingredients - Rosehip Oil, Arginine, and Keratin—to help repair, strengthen, and protect hair from the cumulative effects of daily styling. Protective Lipid: The exact kind found in healthy hair, acts as the first line of defence to help protect hair against damage. Moringa Seed Oil: Helps provide shine and softness with antioxidants, Vitamins A and E, Zinc, and Silica –ingredients that are fundamental to creating healthy, strong, damage-resistant hair. Arginine: Arginine is a naturally occurring amino acid crucial to hair’s strength. Products that include Arginine help protect hair and rebuild it from the inside out. Ingredients Aqua (Water, Eau), Butylene Glycol, Dimethicone, Sorbitol, Behenyl Alcohol, Stearyl Alcohol, Behentrimonium Chloride, Cetyl Alcohol, Glyceryl Oleate, Parfum (Fragrance), Aminopropyl Dimethicone, Isopropyl Alcohol, Phenoxyethanol, Stearyl Dihydroxypropyldimonium Oligosaccharides, Steartrimonium Chloride, Octyldodecanol, Propylene Glycol, Arginine, Cocos Nucifera (Coconut) Oil, Moringa Oleifera Seed Oil, Citric Acid, Dipropylene Glycol, Peg-6 Methyl Ether Dimethicone, C10-40 Isoalkylamidopropylethyldimonium Ethosulfate, Peg-90m, Phosphatidylcholine, Glycerin, Arginine Hcl, Laurdimonium Hydroxypropyl Hydrolyzed Keratin, Avena Sativa (Oat) Peptide, Rosa Canina Fruit Oil, Benzyl Alcohol, Benzoic Acid, Sodium Benzoate, Tocopherol, Sodium Hydroxide, Citronellol, Alpha-isomethyl Ionone73,80 £*Shipping: 0,00 £Secure redirect to the provider
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How was the supremum of the inequality determined?
The supremum of an inequality is determined by finding the smallest upper bound of the set of values that satisfy the inequality. This is done by analyzing the inequality and finding the maximum value that still satisfies the inequality. In some cases, this can be done algebraically by solving for the maximum value, while in other cases it may require using calculus or other mathematical techniques to find the supremum. Once the supremum is determined, it represents the smallest value that the set of values can approach without violating the inequality. **
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Is the supremum of the following set not 2?
The supremum of a set is the least upper bound of the set. If the set contains an element that is greater than 2, then the supremum of the set cannot be 2. However, if all the elements in the set are less than or equal to 2, then the supremum of the set could be 2. Therefore, without knowing the specific elements of the set, it is not possible to definitively say whether the supremum of the set is not 2. **
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What are the supremum and infimum of this sequence?
The supremum of a sequence is the smallest real number that is greater than or equal to every term in the sequence. The infimum is the largest real number that is less than or equal to every term in the sequence. To find the supremum and infimum of a sequence, we need to find the maximum and minimum values of the sequence. If the sequence is bounded, then the supremum and infimum will be the maximum and minimum values of the sequence, respectively. If the sequence is unbounded, then the supremum and infimum may not exist. **
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What is the difference between supremum and limit superior?
The supremum of a set is the least upper bound of the set, meaning it is the smallest number that is greater than or equal to all the numbers in the set. The limit superior of a sequence is the largest limit point of the sequence, meaning it is the largest number that the sequence gets arbitrarily close to as the index goes to infinity. In other words, the supremum is a property of a set, while the limit superior is a property of a sequence. **
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