By L. de Branges

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This text discusses a few tools of describing and pertaining to mathematical items and of always and unambiguously signaling the logical constitution of mathematical arguments.

Extra resources for Cardinality and Invariant Subspaces

Sample text

When you put a number in the top it multiplies it by 5 then sends the new number out the side. 2 IN H5 Advancing Mathematician OUT 10 50 OUT 6 11 3 7 1 Mahobe Resources (NZ) Ltd Multiplication Practice Write in the missing numbers. 6+6 2H............ = ............ 4+4+4 3H............ = ............ H............ = ............ H............ = ............ H............ = ............ Fill in the boxes. You will need to know the 1H, 2H, 3H, 4H, 5H and 10H tables. 9H 4H 5H 7H 3H Mahobe Resources (NZ) Ltd 8H 5H 6H 10H 12H =18 =16 =10 =70 =15 51 =24 =25 =18 =40 =60 Advancing Mathematician Multiplication Practice Write in the missing numbers.

Circle the odd numbers. 17 98 54 12 9 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 3233 34 3536 37 38 39 40 41 42 43 44 45 46 4748 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 63 64 65 ............................ 2 66 25 7 4 32 73 1 80 19 Mahobe Resources (NZ) Ltd 34 68 is between 67 and 69. 50 is between 49 and 51. 71 and ........ 73 72 is between ........

44 11 squares ............. 48 48 12 squares ............. sides 12H4=............. 46 Advancing Mathematician OUT 33 6 27 28 7H4=............. 12 18 32 8H4=............. 24 6H4=............. 48 12H4=............. Multiplication Tables 12H4= 48 Do the multiplications by counting the groups of dots. 2H4= 8 5H4= 20 Complete the table. 10 IN OUT 44 11H4=............. 5 1H5=............. 10 2H5=............. 15 3H5=............. 20 4H5=............. 11H4= 44 H4 40 10H4=............. 45 8H4= 32 Write in the missing numbers.