In Mathematics, 1 divided by 0 is undefined. Division involves splitting something into equal parts, but dividing by 0 means no parts exist to divide into. Thus, it is conceptually impossible, to break the rules of arithmetic and logic.<\/p>\n\n\n\n
Complete Answer:<\/strong><\/p>\n\n\n\n Let\u2019s carefully go step by step to understand what 1 divided by 0 means<\/strong> and why it\u2019s undefined.<\/p>\n\n\n\n Step 1: Understanding Division<\/strong><\/p>\n In any division, we deal with:<\/p>\n The goal of division is to find a number such that:<\/p>\n Step 2: Setting Up the Equation<\/strong><\/p>\n Let\u2019s assume the result of Step 3: Solving the Equation<\/strong><\/p>\n Key Property of Zero:<\/strong> Any number multiplied by From the equation <\/p>\n Step 4: Special Cases to Consider<\/strong><\/p>\n If <\/strong> The equation becomes If <\/strong> Any number multiplied by What if <\/strong> In theory, dividing <\/p>\n Step 5: Summary<\/strong><\/p>\n Why is <\/strong> Division requires finding a number Therefore, Step 6: A Note on Limits<\/p>\n In calculus, when dividing by numbers very close to As the divisor approaches In normal arithmetic (without limits), <\/p>\n Final Answer:<\/strong><\/p>\n Common Maths Questions:<\/strong><\/p>\n\n\n\n\n
1<\/code>).<\/li>\n 0<\/code>).<\/li>\n 1 \u00f7 0<\/code> is some real number x<\/code>. Then:<\/p>\n0<\/code> is always 0<\/code>. For example:<\/p>\n1 = 0 \u00d7 x<\/code>, we are trying to find a number x<\/code> such that multiplying it by 0<\/code> gives 1<\/code>. This is impossible<\/strong>, because no real number satisfies this condition.<\/p>\n\n
x = 0<\/strong><\/code>:<\/strong><\/p>\n 1 = 0 \u00d7 0 = 0<\/code>, which is not true. So x \u2260 0<\/code>.<\/p>\n <\/li>\n x<\/strong><\/code> is any non-zero real number:<\/strong><\/p>\n 0<\/code> is still 0<\/code>, not 1<\/code>. Hence, no real number x<\/code> works.<\/p>\n <\/li>\n x<\/strong><\/code> could be \u201cinfinity\u201d?<\/strong><\/p>\n 1<\/code> by smaller and smaller numbers (like 0.1, 0.01, 0.001<\/code>) results in larger and larger values. However, in pure mathematics, infinity is not a real number\u2014it\u2019s a concept. Therefore, division by 0<\/code> is still undefined<\/strong>.<\/p>\n <\/li>\n<\/ol>\n1 \u00f7 0<\/strong><\/code> Undefined?<\/strong><\/p>\nx<\/code> such that multiplying it by 0<\/code> equals 1<\/code>. This is not possible<\/strong> in the real number system, as 0 \u00d7 x = 0<\/code> for all values of x<\/code>.<\/p>\n1 \u00f7 0<\/code> is undefined<\/strong> in the set of real numbers.<\/p>\n0<\/code> (but not exactly 0<\/code>), the result becomes arbitrarily large. For example:<\/p>\n0<\/code>, the result approaches infinity. However, this is only valid in the concept of limits<\/strong>, where we say:<\/p>\n1 \u00f7 0<\/code> is still undefined<\/strong>.<\/p>\n