Endlessness is probably the most profound and challenging idea of basic maths. The mind finds (a)it difficult to cope with the idea of something going on for ever. What, for example, would happen ( 1 ) we start counting 1,2,3,4,5…and never stop? I remember asking this seemingly simple question ( 2 ) a child, and receiving ( 3 ) straightforward answer. The default response from parents and schoolteachers was that we get to ‘infinity’ but this ( 4 ) essentially just restates the question. Infinity is simply ( 5 ) as being the number that we get to when we start counting and never stop.

Nevertheless, we are told from a relatively ( 6 ) age to treat infinity like a number, a weird number, but a number all the same. We are shown the ( 7 ) for infinity, the endless loop $\infty$(called a 'lemniscate’), and taught its peculiar arithmetic. Add any finite number ( 8 ) infinity. and we get infinity. Subtract any finite number from infinity and we get infinity. Multiply or ( 9 ) infinity by a finite number, as ( 10 ) as it isn't zero, and the result is also infinity.(b)The ease with which we are told that infinity is a number disguises more than 2000 years of struggling to come to terms with its mysteries.

• maths:数学
• default:標準的な
• restates:言い換える
• weird:奇妙な
• arithmetic:計算
• disguises:隠す

1. 文中の空所(1)～(10)に入る適当な語を下から選び解答欄に記入しなさい。
   [
   • answer
   • as
   • defined
   • divide
   • early
   • if
   • long
   • no
   • symbol
   • to
   • ]
2. 下線(a)itが何を指すか日本語で書きなさい。
3. 文中の下線部(b)を日本語に訳しなさい。